OEIS/Cumulative counting - Revision history

imported>Gfis: /* List of cumulative counting sequences */

2021-12-29T17:25:55Z

List of cumulative counting sequences

← Older revision		Revision as of 17:25, 29 December 2021
Line 24:		Line 24:
	* a major rule name (A, B were defined by C. Kimberling)		* a major rule name (A, B were defined by C. Kimberling)
	* the starting value s(1)		* the starting value s(1)
	* a code for the ordering in the ~~segements~~ (increasing/decreasing order, first appearance)		* a code for the ordering in the segments (increasing/decreasing order, first appearance)
	* a code for the row number (1, 2, ...)		* a code for the row number (1, 2, ...)
	* optional parameters		* optional parameters
Line 150:		Line 150:
	[http://oeis.org/A240508 A240508] T 0 io 5 with0=3		[http://oeis.org/A240508 A240508] T 0 io 5 with0=3
	122 sequences		122 sequences

	==Symmetry and relations==		==Symmetry and relations==
	s A 1 A 2 T I J K P 1 P 2 P 3 P 4		s A 1 A 2 T I J K P 1 P 2 P 3 P 4

imported>Gfis: 126 => more than 120

2018-05-01T08:57:56Z

126 => more than 120

← Older revision		Revision as of 08:57, 1 May 2018
Line 20:		Line 20:
	# In the example for [https://oeis.org/A055168 A055168], the last <code>3</code> should be a <code>4</code>.		# In the example for [https://oeis.org/A055168 A055168], the last <code>3</code> should be a <code>4</code>.
	==List of ''cumulative counting'' sequences==		==List of ''cumulative counting'' sequences==
	The list of ~~116~~ sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):		The list of more than 120 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):
	* the OEIS A-number,		* the OEIS A-number,
	* a major rule name (A, B were defined by C. Kimberling)		* a major rule name (A, B were defined by C. Kimberling)
Line 150:		Line 150:
	[http://oeis.org/A240508 A240508] T 0 io 5 with0=3		[http://oeis.org/A240508 A240508] T 0 io 5 with0=3
	122 sequences		122 sequences
			==Symmetry and relations==
	s A 1 A 2 T I J K P 1 P 2 P 3 P 4		s A 1 A 2 T I J K P 1 P 2 P 3 P 4
	1 [http://oeis.org/A030707 A030707] [http://oeis.org/A030708 A030708] [http://oeis.org/A030709 A030709] [http://oeis.org/A030710 A030710] [http://oeis.org/A030711 A030711] [http://oeis.org/A030712 A030712] [http://oeis.org/A030713 A030713] [http://oeis.org/A030714 A030714] [http://oeis.org/A030715 A030715] [http://oeis.org/A030716 A030716] io		1 [http://oeis.org/A030707 A030707] [http://oeis.org/A030708 A030708] [http://oeis.org/A030709 A030709] [http://oeis.org/A030710 A030710] [http://oeis.org/A030711 A030711] [http://oeis.org/A030712 A030712] [http://oeis.org/A030713 A030713] [http://oeis.org/A030714 A030714] [http://oeis.org/A030715 A030715] [http://oeis.org/A030716 A030716] io

imported>Gfis: /* Symmetry */ observed

2018-05-01T08:56:39Z

Symmetry: observed

← Older revision		Revision as of 08:56, 1 May 2018
Line 150:		Line 150:
	[http://oeis.org/A240508 A240508] T 0 io 5 with0=3		[http://oeis.org/A240508 A240508] T 0 io 5 with0=3
	122 sequences		122 sequences
	~~==Symmetry==~~
	s A 1 A 2 T I J K P 1 P 2 P 3 P 4		s A 1 A 2 T I J K P 1 P 2 P 3 P 4
	1 [http://oeis.org/A030707 A030707] [http://oeis.org/A030708 A030708] [http://oeis.org/A030709 A030709] [http://oeis.org/~~A030711~~ A030710] [http://oeis.org/A030711 A030711] [http://oeis.org/A030712 A030712] [http://oeis.org/A030713 A030713] [http://oeis.org/A030714 A030714] [http://oeis.org/A030715 A030715] [http://oeis.org/A030716 A030716] io		1 [http://oeis.org/A030707 A030707] [http://oeis.org/A030708 A030708] [http://oeis.org/A030709 A030709] [http://oeis.org/A030710 A030710] [http://oeis.org/A030711 A030711] [http://oeis.org/A030712 A030712] [http://oeis.org/A030713 A030713] [http://oeis.org/A030714 A030714] [http://oeis.org/A030715 A030715] [http://oeis.org/A030716 A030716] io
	[http://oeis.org/A030717 A030717] [http://oeis.org/A030718 A030718] [http://oeis.org/A030719 A030719] [http://oeis.org/A030720 A030720] [http://oeis.org/A030721 A030721] [http://oeis.org/A030722 A030722] [http://oeis.org/A030723 A030723] [http://oeis.org/A030724 A030724] [http://oeis.org/A030725 A030725] [http://oeis.org/A030726 A030726] io		[http://oeis.org/A030717 A030717] [http://oeis.org/A030718 A030718] [http://oeis.org/A030719 A030719] [http://oeis.org/A030720 A030720] [http://oeis.org/A030721 A030721] [http://oeis.org/A030722 A030722] [http://oeis.org/A030723 A030723] [http://oeis.org/A030724 A030724] [http://oeis.org/A030725 A030725] [http://oeis.org/A030726 A030726] io
	3 [http://oeis.org/A030727 A030727] [http://oeis.org/A030728 A030728] [http://oeis.org/A030729 A030729] [http://oeis.org/A030730 A030730] [http://oeis.org/A030731 A030731] [http://oeis.org/A030732 A030732] [http://oeis.org/A030733 A030733] [http://oeis.org/A030734 A030734] [http://oeis.org/A030735 A030735] [http://oeis.org/A030736 A030736] io		3 [http://oeis.org/A030727 A030727] [http://oeis.org/A030728 A030728] [http://oeis.org/A030729 A030729] [http://oeis.org/A030730 A030730] [http://oeis.org/A030731 A030731] [http://oeis.org/A030732 A030732] [http://oeis.org/A030733 A030733] [http://oeis.org/A030734 A030734] [http://oeis.org/A030735 A030735] [http://oeis.org/A030736 A030736] io
Line 170:		Line 169:
	4 [http://oeis.org/A055180 A055180] [http://oeis.org/A055181 A055181] [http://oeis.org/A055182 A055182] fa		4 [http://oeis.org/A055180 A055180] [http://oeis.org/A055181 A055181] [http://oeis.org/A055182 A055182] fa
	5 [http://oeis.org/A055183 A055183] [http://oeis.org/A055184 A055184] [http://oeis.org/A055185 A055185] fa		5 [http://oeis.org/A055183 A055183] [http://oeis.org/A055184 A055184] [http://oeis.org/A055185 A055185] fa
	As can be ~~seen from these tables and the parameters, there are the following relations~~:		The following relations can be observed:
	A030709 = A030759		1 A030709 = A030759 (segment lengths)
	A030729 = A030779		2 A030739 = A030769
	A030749 = A030789		3 A030729 = A030779
	A030711 = A030761		4 A030749 = A030789
			1 A030711 = A030761 (next term which is greater than all previous)

	==Generating Perl program==		==Generating Perl program==

imported>Gfis at 08:27, 1 May 2018

2018-05-01T08:27:43Z

@@ Line 16: / Line 16: @@
 # Most b-files are rather short, though some sequences have quite a number of terms in common (e.g. 61, 82) before they start to differ.
 # [https://oeis.org/A030717 A030717] (row 1)  does not correspond with the derived sequences [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.
-# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.
+# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>OFFSET 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.
-# A030709 = A030759, A030729 = A030779, A030749 = A030789, A030711 = A030761
+# [https://oeis.org/A055186 A055186] should not carry KEYWORD <code>base</code>.
-# [https://oeis.org/A055186 A055186] should not carry keyword <code>base</code>.
+# In the example for [https://oeis.org/A055168 A055168], the last <code>3</code> should be a <code>4</code>.
 ==List of ''cumulative counting'' sequences==
 The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):
@@ Line 151: / Line 150: @@
   [http://oeis.org/A240508 A240508] T 0 io 5 with0=3
 sequences
 ==Generating Perl program==
 The Perl program below can be used to generate all sequences of the list. It produces b-files, but the rules T, J, K are currently rather slow, and take time above 100 entries. The latest version of the program and its auxilliary files can be found on a [https://github.com/gfis/fasces/tree/master/oeis/A055187 Github repository].

imported>Gfis at 09:32, 30 April 2018

2018-04-30T09:32:07Z

← Older revision		Revision as of 09:32, 30 April 2018
Line 18:		Line 18:
	# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.		# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.
	# A030709 = A030759, A030729 = A030779, A030749 = A030789, A030711 = A030761		# A030709 = A030759, A030729 = A030779, A030749 = A030789, A030711 = A030761
	# [https://oeis.org/A055186 A055186] should not carry keyword <code>base</~~base~~>.		# [https://oeis.org/A055186 A055186] should not carry keyword <code>base</code>.
			# The example in [https://oeis.org/A055168 A055168] has a typo.
	==List of ''cumulative counting'' sequences==		==List of ''cumulative counting'' sequences==
	The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):		The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):

imported>Gfis: revision, 030717/18/40, 126027,253170 are still bad

2018-04-30T09:30:19Z

revision, 030717/18/40, 126027,253170 are still bad

Show changes

imported>Gfis: heading

2018-04-25T13:51:19Z

heading

← Older revision		Revision as of 13:51, 25 April 2018
Line 137:		Line 137:
	[https://oeis.org/A217760 A217760] Rule A fa 0 9666		[https://oeis.org/A217760 A217760] Rule A fa 0 9666
	[https://oeis.org/A217780 A217780] Rule A fa 1 71		[https://oeis.org/A217780 A217780] Rule A fa 1 71
	=Generating Perl program==		==Generating Perl program==
	The Perl program below can be used to generate all sequences of the list. It produces b-files, but the rules T, J, K are currently rather slow, and take time above 100 entries. The latest version of the program and its auxilliary files can be found on a [https://github.com/gfis/fasces/tree/master/oeis/A055187 Github repository].		The Perl program below can be used to generate all sequences of the list. It produces b-files, but the rules T, J, K are currently rather slow, and take time above 100 entries. The latest version of the program and its auxilliary files can be found on a [https://github.com/gfis/fasces/tree/master/oeis/A055187 Github repository].
	<pre>		<pre>
Line 807:		Line 807:
	== Results and Problems ==		== Results and Problems ==
	The makefile currently generates and compares all 116 sequences in the list. Only a few problems were found:		The makefile currently generates and compares all 116 sequences in the list. Only a few problems were found:
			# Some b-files are rather short, though some sequences have quite a number of terms in common (for example 61) before they start to differ.
	# [https://oeis.org/A030717 A030717] (row 1) does not correspond with the derived sequences and [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.		# [https://oeis.org/A030717 A030717] (row 1) does not correspond with the derived sequences and [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.
	# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.		# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.
			# A030709 = A030759, A030729 = A030779, A030749 = A030789, A030711 = A030761
			# [https://oeis.org/A055186 A055186] should not carry keyword <code>base</base>.

imported>Gfis: description

2018-04-25T08:53:52Z

description

← Older revision		Revision as of 08:53, 25 April 2018
Line 1:		Line 1:
	[https://oeis.org/wiki/User:Clark_Kimberling Clark Kimberling] defined - for example - [https://~~OEIS~~.org/~~A131388 A131388~~] ~~with the following rule~~:		[https://oeis.org/wiki/User:Clark_Kimberling Clark Kimberling] defined - for example - in [https://oeis.org/A217760 A217760]:
	~~Rule 1~~ follows. ~~For k >= 1~~, ~~let~~ A(k) ~~= {a~~(1), ~~…, a(k)} and D(k) = {d(1), …, d(k)}~~. ~~Begin with k = 1 and nonnegative integers a(1) and d(1).~~		Write 0 followed by segments defined inductively as follows: each segment
	~~Step 1: If there is an integer h such that 1 - a(k) < h <~~ 0 ~~and h is not in D(k) and a(k) + h is not in A(k)~~, ~~let d(k+1) be~~ the ~~greatest such h, let a(k+~~1~~) = a(k) + h~~, ~~replace k~~ by ~~k +~~ 1, ~~and repeat Step~~ 1; ~~otherwise do Step 2~~.		tells how many times each previously written integer occurs, in the order
	~~Step 2:~~ ~~Let h be the least positive integer not in D(k) such that a(k) + h is not in A(k)~~. ~~Let a(k+~~1~~) = a(k) + h and d(k+~~1~~) = h~~. ~~Replace k by k+~~1 ~~and do Step~~ 1.		of first occurrence. This is Method A (adjective-before-noun pairs); for
	~~Conjecture: if a(~~1~~) is an nonnegative integer and d(~~1~~) is an integer, then (a(n)) is a permutation of the nonnegative integers (if a(~~1~~) =~~ 0~~) or a permutation of the positive integers (if a(~~1~~) >~~ 0). ~~Moreover, (d(n)) is a permutation of the integers if d(1) =~~ 0~~, or of the nonzero integers if d(~~1~~) > 0.~~		Method B (noun-before-adjective), see A055168.
			Example:
			Start with 0, followed by the adjective-noun pair 1,0; followed by
			adjective-noun pairs 2,0 then 1,1; etc. Writing the pairs vertically,
			the initial segments are
			0.\|.1.\|.2 1.\|.3 3 1.\|.4 5 2 2.\|.5 6 5 3 1 1.\|.6 9 6 5 2 4 1.\|.7 11 8 6 4 6 4 1
			..\|.0.\|.0 1.\|.0 1 2.\|.0 1 2 3.\|.0 1 2 3 4 5.\|.0 1 2 3 4 5 6.\|.0 1 2 3 4 5 6 9

	Depending on the starting ~~values a(1) and d~~(1), ~~and~~ with variations of the rules, there are ~~several dozens of~~ related sequences in the OEIS~~. There are lists of related sequences in [https://oeis.org/A257705 A257705], [https://oeis.org/A257883 A257883] and [https://oeis.org/A257905 A257905]~~.		Depending on the starting value s(1), with variations of the rules and derivations, there are more than 100 related sequences in the OEIS.
	==List of ''cumulative counting'' sequences==		==List of ''cumulative counting'' sequences==
	The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):		The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):
Line 802:		Line 808:
	The makefile currently generates and compares all 116 sequences in the list. Only a few problems were found:		The makefile currently generates and compares all 116 sequences in the list. Only a few problems were found:
	# [https://oeis.org/A030717 A030717] (row 1) does not correspond with the derived sequences and [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.		# [https://oeis.org/A030717 A030717] (row 1) does not correspond with the derived sequences and [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.
	* [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.		# [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.

imported>Gfis: 1st

2018-04-25T08:47:22Z

1st

New page

[https://oeis.org/wiki/User:Clark_Kimberling Clark Kimberling] defined - for example - [https://OEIS.org/A131388 A131388] with the following rule:
Rule 1 follows. For k >= 1, let A(k) = {a(1), …, a(k)} and D(k) = {d(1), …, d(k)}. Begin with k = 1 and nonnegative integers a(1) and d(1).
Step 1: If there is an integer h such that 1 - a(k) < h < 0 and h is not in D(k) and a(k) + h is not in A(k), let d(k+1) be the greatest such h, let a(k+1) = a(k) + h, replace k by k + 1, and repeat Step 1; otherwise do Step 2.
Step 2: Let h be the least positive integer not in D(k) such that a(k) + h is not in A(k). Let a(k+1) = a(k) + h and d(k+1) = h. Replace k by k+1 and do Step 1.
Conjecture: if a(1) is an nonnegative integer and d(1) is an integer, then (a(n)) is a permutation of the nonnegative integers (if a(1) = 0) or a permutation of the positive integers (if a(1) > 0). Moreover, (d(n)) is a permutation of the integers if d(1) = 0, or of the nonzero integers if d(1) > 0.

Depending on the starting values a(1) and d(1), and with variations of the rules, there are several dozens of related sequences in the OEIS. There are lists of related sequences in [https://oeis.org/A257705 A257705], [https://oeis.org/A257883 A257883] and [https://oeis.org/A257905 A257905].
==List of ''cumulative counting'' sequences==
The list of 116 sequences below describes the variations. The list has the following entries (which are explained in more detail in the Perl program, below):
* the OEIS A-number,
* a major rule name (A, B were defined by C. Kimberling)
* a minor rule number, the row number (1, 2, ...)
* a code for the ordering in the segements
* the starting value s(1)
* an optional small integer parameter
* the number of lines in the b-file
[https://oeis.org/A030707 A030707] Rule A.1 io 1 84
[https://oeis.org/A030708 A030708] Rule A.2 io 1 82
[https://oeis.org/A030709 A030709] Rule T io 1 30
[https://oeis.org/A030710 A030710] Rule I.1 io 1 54
[https://oeis.org/A030711 A030711] Rule J.1 io 1 32
[https://oeis.org/A030712 A030712] Rule K.1 io 1 32
[https://oeis.org/A030713 A030713] Rule P.1 io 1 1 52
[https://oeis.org/A030714 A030714] Rule P.1 io 1 2 50
[https://oeis.org/A030715 A030715] Rule P.1 io 1 3 50
[https://oeis.org/A030716 A030716] Rule P.1 io 1 4 49
[https://oeis.org/A030717 A030717] Rule A.3 io 1 1732
[https://oeis.org/A030718 A030718] Rule A.4 io 1
[https://oeis.org/A030719 A030719] Rule T io 1
[https://oeis.org/A030720 A030720] Rule I.3 io 1
[https://oeis.org/A030721 A030721] Rule J.3 io 1
[https://oeis.org/A030722 A030722] Rule K.3 io 1
[https://oeis.org/A030723 A030723] Rule P.3 io 1 1
[https://oeis.org/A030724 A030724] Rule P.3 io 1 2
[https://oeis.org/A030725 A030725] Rule P.3 io 1 3
[https://oeis.org/A030726 A030726] Rule P.3 io 1 4
[https://oeis.org/A030727 A030727] Rule A.1 io 3 83
[https://oeis.org/A030728 A030728] Rule A.2 io 3 83
[https://oeis.org/A030729 A030729] Rule T io 3 29
[https://oeis.org/A030730 A030730] Rule I.1 io 3 53
[https://oeis.org/A030731 A030731] Rule J.1 io 3 29
[https://oeis.org/A030732 A030732] Rule K.1 io 3 29
[https://oeis.org/A030733 A030733] Rule P.1 io 3 1 51
[https://oeis.org/A030734 A030734] Rule P.1 io 3 2 50
[https://oeis.org/A030735 A030735] Rule P.1 io 3 3 46
[https://oeis.org/A030736 A030736] Rule P.1 io 3 4 49
[https://oeis.org/A030737 A030737] Rule A.1 io 2 83
[https://oeis.org/A030738 A030738] Rule A.2 io 2 83
[https://oeis.org/A030739 A030739] Rule T io 2 29
[https://oeis.org/A030740 A030740] Rule I.1 io 2 53
[https://oeis.org/A030741 A030741] Rule J.1 io 2 30
[https://oeis.org/A030742 A030742] Rule K.1 io 2 30
[https://oeis.org/A030743 A030743] Rule P.1 io 2 1 52
[https://oeis.org/A030744 A030744] Rule P.1 io 2 2 50
[https://oeis.org/A030745 A030745] Rule P.1 io 2 3 49
[https://oeis.org/A030746 A030746] Rule P.1 io 2 4 49
[https://oeis.org/A030747 A030747] Rule A.1 io 4 82
[https://oeis.org/A030748 A030748] Rule A.2 io 4 86
[https://oeis.org/A030749 A030749] Rule T io 4 30
[https://oeis.org/A030750 A030750] Rule I.1 io 4 53
[https://oeis.org/A030751 A030751] Rule J.1 io 4 29
[https://oeis.org/A030752 A030752] Rule K.1 io 4 29
[https://oeis.org/A030753 A030753] Rule P.1 io 4 1 51
[https://oeis.org/A030754 A030754] Rule P.1 io 4 2 49
[https://oeis.org/A030755 A030755] Rule P.1 io 4 3 46
[https://oeis.org/A030756 A030756] Rule P.1 io 4 4 33
[https://oeis.org/A030757 A030757] Rule A.1 do 1 84
[https://oeis.org/A030758 A030758] Rule A.2 do 1 81
[https://oeis.org/A030759 A030759] Rule T do 1 29
[https://oeis.org/A030760 A030760] Rule I.1 do 1 53
[https://oeis.org/A030761 A030761] Rule J.1 do 1 29
[https://oeis.org/A030762 A030762] Rule K.1 do 1 29
[https://oeis.org/A030763 A030763] Rule P.1 do 1 1 52
[https://oeis.org/A030764 A030764] Rule P.1 do 1 2 50
[https://oeis.org/A030765 A030765] Rule P.1 do 1 3 50
[https://oeis.org/A030766 A030766] Rule P.1 do 1 4 49
[https://oeis.org/A030767 A030767] Rule A.1 do 2 86
[https://oeis.org/A030768 A030768] Rule A.2 do 2 81
[https://oeis.org/A030769 A030769] Rule T do 2 29
[https://oeis.org/A030770 A030770] Rule I.1 do 2 53
[https://oeis.org/A030771 A030771] Rule J.1 do 2 36
[https://oeis.org/A030772 A030772] Rule K.1 do 2 36
[https://oeis.org/A030773 A030773] Rule P.1 do 2 1 52
[https://oeis.org/A030774 A030774] Rule P.1 do 2 2 51
[https://oeis.org/A030775 A030775] Rule P.1 do 2 3 49
[https://oeis.org/A030776 A030776] Rule P.1 do 2 4 49
[https://oeis.org/A030777 A030777] Rule A.1 do 3 85
[https://oeis.org/A030778 A030778] Rule A.2 do 3 81
[https://oeis.org/A030779 A030779] Rule T do 3 29
[https://oeis.org/A030780 A030780] Rule I.1 do 3 53
[https://oeis.org/A030781 A030781] Rule J.1 do 3 29
[https://oeis.org/A030782 A030782] Rule K.1 do 3 29
[https://oeis.org/A030783 A030783] Rule P.1 do 3 1 52
[https://oeis.org/A030784 A030784] Rule P.1 do 3 2 50
[https://oeis.org/A030785 A030785] Rule P.1 do 3 3 49
[https://oeis.org/A030786 A030786] Rule P.1 do 3 4 49
[https://oeis.org/A030787 A030787] Rule A.1 do 4 83
[https://oeis.org/A030788 A030788] Rule A.2 do 4 83
[https://oeis.org/A030789 A030789] Rule T do 4 30
[https://oeis.org/A030790 A030790] Rule I.1 do 4 53
[https://oeis.org/A030791 A030791] Rule J.1 do 4 30
[https://oeis.org/A030792 A030792] Rule K.1 do 4 30
[https://oeis.org/A030793 A030793] Rule P.1 do 4 1 51
[https://oeis.org/A030794 A030794] Rule P.1 do 4 2 49
[https://oeis.org/A030795 A030795] Rule P.1 do 4 3 46
[https://oeis.org/A030796 A030796] Rule P.1 do 4 4 33
[https://oeis.org/A055168 A055168] Rule B fa 0 90
[https://oeis.org/A055169 A055169] Rule N fa 0 10000
[https://oeis.org/A055170 A055170] Rule D fa 0 6000
[https://oeis.org/A055171 A055171] Rule B fa 1 87
[https://oeis.org/A055172 A055172] Rule N fa 1 39
[https://oeis.org/A055173 A055173] Rule D fa 1 64
[https://oeis.org/A055174 A055174] Rule B fa 2 88
[https://oeis.org/A055175 A055175] Rule N fa 2 39
[https://oeis.org/A055176 A055176] Rule D fa 2 64
[https://oeis.org/A055177 A055177] Rule B fa 3 87
[https://oeis.org/A055178 A055178] Rule N fa 3 39
[https://oeis.org/A055179 A055179] Rule D fa 3 64
[https://oeis.org/A055180 A055180] Rule B fa 4 88
[https://oeis.org/A055181 A055181] Rule N fa 4 39
[https://oeis.org/A055182 A055182] Rule D fa 4 64
[https://oeis.org/A055183 A055183] Rule B fa 5 87
[https://oeis.org/A055184 A055184] Rule N fa 5 39
[https://oeis.org/A055185 A055185] Rule D fa 5 64
[https://oeis.org/A055186 A055186] Rule A iz 0 1022
[https://oeis.org/A055187 A055187] Rule A io 1 98
[https://oeis.org/A055188 A055188] Rule A fa 2 87
[https://oeis.org/A055189 A055189] Rule A fa 3 87
[https://oeis.org/A055190 A055190] Rule A fa 4 89
[https://oeis.org/A055191 A055191] Rule A fa 5 87
[https://oeis.org/A217760 A217760] Rule A fa 0 9666
[https://oeis.org/A217780 A217780] Rule A fa 1 71
=Generating Perl program==
The Perl program below can be used to generate all sequences of the list. It produces b-files, but the rules T, J, K are currently rather slow, and take time above 100 entries. The latest version of the program and its auxilliary files can be found on a [https://github.com/gfis/fasces/tree/master/oeis/A055187 Github repository].
<pre>
<nowiki>
#!perl

# Generate OEIS A030707, A055187, A217760 and related
# "cumulative counting" sequences as defined by Clark Kimberling.
# http://faculty.evansville.edu/ck6/integer/unsolved.html, Problem 4
# @(#) $Id$
# 2018-04-20, Georg Fischer
#------------------------------------------------------
# Comment from A217760:
# Write 0 followed by segments defined inductively as follows: each segment
# tells how many times each previously written integer occurs, in the order
# of first occurrence. This is Method A (adjective-before-noun pairs); for
# Method B (noun-before-adjective), see A055168.
# Example:
# Start with 0, followed by the adjective-noun pair 1,0; followed by
# adjective-noun pairs 2,0 then 1,1; etc. Writing the pairs vertically,
# the initial segments are
# 0.|.1.|.2 1.|.3 3 1.|.4 5 2 2.|.5 6 5 3 1 1.|.6 9 6 5 2 4 1.|.7 11 8 6 4 6 4 1
# ..|.0.|.0 1.|.0 1 2.|.0 1 2 3.|.0 1 2 3 4 5.|.0 1 2 3 4 5 6.|.0 1 2 3 4 5 6 9
#
# Usage:
# perl cumulcount.pl rule row noeis len order p1 [p2 [debug]]
# rule = "A" (attribute before noun)
# "B" (noun before attribute)
# "D" (new, distinct elements)
# "I" (inverse, first occurrence of a number)
# "J" (next term which is greater than all previous)
# "K" (next position where term is greater than all previous)
# "N" (number of new elements in segment)
# "P" (positions of small numbers (p2))
# "T" (number of terms in segment n)
# row = 0 (both)
# 1 (first)
# 2 (second)
# 3 (first, count in first only)
# 4 (second, count in first only)
# noeis = "030707|055187|217760 ..." (OEIS number without "A")
# len = length of sequence to be generated
# order = "io" (increasing order)
# "do" (decreasing order)
# "iz" (increasing order, complete with zero counts)
# "dz" (decreasing order, complete with zero counts)
# "fa" (order of first appearance)
# p1 = starting value for a(1): 0, 1, 3, 4, 5
# p2 = 2nd parameter (for rule "P"): 1, 2, 3, 4
# debug = 0 (none)
# 1 (with segments)
#--------------------------------------------------------
use strict;

my $rule = "A"; if (scalar(@ARGV) > 0) { $rule = shift(@ARGV); }
my $row = 0; if (scalar(@ARGV) > 0) { $row = shift(@ARGV); }
my $noeis = ""; if (scalar(@ARGV) > 0) { $noeis = shift(@ARGV); }
my $len = 256; if (scalar(@ARGV) > 0) { $len = shift(@ARGV); }
my $order = "io"; if (scalar(@ARGV) > 0) { $order = shift(@ARGV); }
my $p1 = 1; if (scalar(@ARGV) > 0) { $p1 = shift(@ARGV); }
my $p2 = 0; if (scalar(@ARGV) > 0) { $p2 = shift(@ARGV); }
my $debug = 0; if (scalar(@ARGV) > 0) { $debug = shift(@ARGV); }

# segments have 2 rows:
# row 1 = attrs
# row 2 = nouns
my $attr;
my $noun;
my %nouns;
my %occrs = (); # first occurrences of attributes
my @seql = (); # sequence list
push(@seql, $p1, 1, $p1);
# 0 1 2 3
my $segno = 1;
my $sseg = 1; # index of 1st element in segment
my $eseg = scalar(@seql); # index of 1st element behind segment
my $inoun;
my $sum;
my $search = $p2; # for $rule =~ m{P}
my $curmax = 0;
my ($sec, $min, $hour, $mday, $mon, $year, $wday, $yday, $isdst)
= localtime (time);
my $timestamp = sprintf ("%04d-%02d-%02d %02d:%02d"
, $year + 1900, $mon + 1, $mday, $hour, $min);
print <<"GFis";
# http://oeis.org/A$noeis/b$noeis.txt: table n,a(n)
# Generated by cumulcount.pl on $timestamp
GFis
my $k = 1;
my $k2 = $k; # copy of k, running as if it were rule A
if (0) {
} elsif ($rule =~ m{[ABIJKP]}i) {
if ($row <= 1) {
&bfile($p1);
}
&bfile(1, $p1);
} elsif ($rule =~ m{D}i) {
print "$k $p1\n"; $k ++;
} elsif ($rule =~ m{N}i) {
print "$k 1\n" ; $k ++;
} elsif ($rule =~ m{T}i) {
print "$k $p1\n"; $k ++;
} else {
die "invalid rule \"$rule\"\n";
}
$segno ++;
while ($k <= $len) { # fill b-file
my %nouns = ();
$inoun = $sseg;
while ($inoun < $eseg) { # count the present nouns (row 2)
my $attr = $seql[$inoun + 0];
my $noun = $seql[$inoun + 1];
if (1) {
$sum = $attr + &count(2, $noun, $sseg, $eseg);
$nouns{$noun} = $sum;
push(@seql, $sum, $noun);
}
$inoun += 2;
} # while $inoun
$inoun = $sseg;
my $start_new = scalar(@seql);
while ($inoun < $eseg) { # count the new attributes (row 1)
my $attr = $seql[$inoun + 0];
if (! defined($nouns{$attr})) {
$sum = &count(1, $attr, $sseg, $eseg);
$nouns{$attr} = $sum;
push(@seql, $sum, $attr);
}
$inoun += 2;
} # while $inoun

if (0) {
} elsif ($order eq "fa") { # order of first appearance
# already stored in @seql
} elsif ($order eq "do") { # decreasing order
$inoun = $eseg;
foreach $noun (sort {$b <=> $a} (keys(%nouns))) { # reverse sort
$seql[$inoun + 0] = $nouns{$noun};
$seql[$inoun + 1] = $noun;
$inoun += 2;
} # foreach
} elsif ($order eq "io") { # increasing order
$inoun = $eseg;
foreach $noun (sort {$a <=> $b} (keys(%nouns))) {
$seql[$inoun + 0] = $nouns{$noun};
$seql[$inoun + 1] = $noun;
$inoun += 2;
} # foreach
} elsif ($order eq "dz") { # decreasing order (complete) - insert 0 counts
my $cnoun = 0; # avoids "while" in first "foreach"
$inoun = $eseg;
foreach $noun (sort {$b <=> $a} (keys(%nouns))) { # reverse sort
while ($cnoun > $noun) {
$seql[$inoun + 0] = 0;
$seql[$inoun + 1] = $cnoun;
$cnoun --;
$inoun += 2;
} # while $cnoun
$seql[$inoun + 0] = $nouns{$noun};
$seql[$inoun + 1] = $noun;
$inoun += 2;
$cnoun = $noun - 1;
} # foreach
} elsif ($order eq "iz") { # increasing order (complete) - insert 0 counts
my $cnoun = $seql[$sseg + 1];
$inoun = $eseg;
foreach $noun (sort {$a <=> $b} (keys(%nouns))) {
while ($cnoun < $noun) {
$seql[$inoun + 0] = 0;
$seql[$inoun + 1] = $cnoun;
$cnoun ++;
$inoun += 2;
} # while $cnoun
$seql[$inoun + 0] = $nouns{$noun};
$seql[$inoun + 1] = $noun;
$inoun += 2;
$cnoun = $noun + 1;
} # foreach
} else {
die "invalid paramter op=\"$order\"\n";
}

if ($debug >= 1) {
print "# segment $segno:";
$inoun = $eseg;
while ($inoun < scalar(@seql)) { #
my $attr = $seql[$inoun + 0];
my $noun = $seql[$inoun + 1];
print " $attr.$noun";
$inoun += 2;
} # while $inoun
print "\n";
} # debug

if (0) {
} elsif ($rule =~ m{[ABIJKP]}i) { # first or second row or both
$inoun = $eseg;
while ($inoun < scalar(@seql)) {
my $attr = $seql[$inoun + 0];
my $noun = $seql[$inoun + 1];
&bfile($attr, $noun);
$inoun += 2;
} # while $inoun
} elsif ($rule =~ m{D}i) { # new terms
$inoun = $start_new;
while ($inoun < scalar(@seql)) {
my $attr = $seql[$inoun + 0];
my $noun = $seql[$inoun + 1];
&bfile($noun);
$inoun += 2;
} # while $inoun
} elsif ($rule =~ m{N}i) { # no. of new terms in segment
my $no_new = (scalar(@seql) - $start_new) >> 1;
&bfile($no_new);
} elsif ($rule =~ m{T}i) { # no. of terms in segemnt
my $no_new = (scalar(@seql) - $eseg) >> 1;
&bfile($no_new);
}
$sseg = $eseg;
$eseg = scalar(@seql);
$segno ++;
} # while b-file

if ($rule =~ m{I}i) { # special treatment of the inverse
$k = 1;
foreach $attr (sort {$a <=> $b} (keys(%occrs))) {
# last if $attr > $k; # must be monotone
print "$k $occrs{$attr}\n"; $k ++;
} # foreach
} # rule I
#----------------
sub bfile {
my ($attr, $noun) = @_;
if (0) {
} elsif ($rule =~ m{P}i) {
if ($attr == $search) {
print "$k $k2\n"; $k ++;
}
$k2 ++;
} elsif ($rule =~ m{I}i) {
if (! defined($occrs{$attr})) {
# assume that rule "I" is called with row=1 only !
$occrs{$attr} = $k;
if ($debug >= 1) {
print "# stored $k in occrs{$attr}\n";
}
}
$k ++;
} elsif ($rule =~ m{J}i) {
if ($attr > $curmax) {
print "$k $attr\n"; $k ++;
$curmax = $attr;
}
$k2 ++;
} elsif ($rule =~ m{k}i) {
if ($attr > $curmax) {
print "$k $k2\n"; $k ++;
$curmax = $attr;
}
$k2 ++;
} elsif (scalar(@_) == 1) {
print "$k $attr\n"; $k ++;
} elsif ($rule =~ m{[DNT]}i) {
# c.f. above
} elsif ($rule =~ m{[A]}i) { # attribute before noun
if (0) {
} elsif ($row == 0) {
print "$k $attr\n"; $k ++;
print "$k $noun\n"; $k ++;
} elsif ($row == 1) {
print "$k $attr\n"; $k ++;
} elsif ($row == 2) {
print "$k $noun\n"; $k ++;
}
} elsif ($rule =~ m{B}i) { # noun before attribute
if (0) {
} elsif ($row == 0) {
print "$k $noun\n"; $k ++;
print "$k $attr\n"; $k ++;
} elsif ($row == 1) {
print "$k $noun\n"; $k ++;
} elsif ($row == 2) {
print "$k $attr\n"; $k ++;
}
} else {
die "invalid rule \"$rule\"\n";
}
} # bfile
#----------------
sub count {
my ($row, $value, $sseg, $eseg) = @_;
my $sum = 0;
if (($rule !~ m{C}i) or ($row == 1)) { #
my $iseg = $sseg;
while ($iseg < $eseg) {
if ($seql[$iseg] == $value) { # attr or noun
$sum ++;
}
$iseg ++;
if ($rule eq "C") {
$iseg ++;
}
} # while $iseg
} # if cond
return $sum;
} # sub count
__DATA__
Rule A, A055187:
1 | 1 | 3 | 4 1 | 6 2 1 | 8 1 3 2 1 |
| 1 | 1 | 1 3 | 1 3 4 | 1 2 3 4 6 |

| 11 3 5 3 2 1 | 13 5 8 4 1 3 2 1 |
| 1 2 3 4 6 8 | 1 2 3 4 5 6 8 11 |

| 16 7 10 6 3 4 4 2 1 |
| 1 2 3 4 5 6 8 11 13 |

| 18 9 12 9 4 6 1 5 1 3 2 1 |
| 1 2 3 4 5 6 7 8 10 11 13 16 |

| 22 11 14 11 6 8 2 6 2 2 4 1 3 2 1 |
| 1 2 3 4 5 6 7 8 9 10 11 12 13 16 18 |

| 25 16 16 14 ...
| 1 2 3 4 ...

--------------------
Rule C; A030717 (row 1), A030718 (row2) - zeroes are inconsistent
1 | 1 | 2 | 2, 1 | 3, 2 | 3, 3, 1 | 4, 3, 3 | 4, 3, 5, 1 | 5, 3, 6, 2, 1
| 1 | 1 | 1, 2 | 1, 2 | 1, 2, 3 | 1, 2, 3 | 1, 2, 3, 4 | 1, 2, 3, 4, 5

| 6, 4, 7, 2, 2, 1 | 7, 6, 7, 3, 2, 2, 1| 8, 8, 8, 3, 2, 3, 3
| 1, 2, 3, 4, 5, 6 | 1, 2, 3, 4, 5, 6, 7| 1, 2, 3, 4, 5, 6, 7

| 8, 9, 11, 3, 2, 3, 3, 3 | 8, 10, 15, 3, 2, 3, 3, 4, 1, 0, 1
| 1, 2, 3, 4, 5, 6, 7, 8 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 11

| 10, 11, 18, 4, 2, 3, 3, 5, 1, 1, 1, 0, 0, 0, 1
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15

| 14, 12, 20, 5, 3, 3, 3, 5, 1, 2, 2, 0, 0, 0, 1, 0, 0, 1
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18

| 17, 14, 23, 5, 5
| 1, 2, 3 ...
# https://oeis.org/wiki/User:Georg_Fischer Feb. 24, 2018
</nowiki>
</pre>
== makefile ==
A Unix <code>makefile</code> was used
* to produce the list of sequences,
* to download (once) the corresponding b-files,
* to regenerate the particular sequences and
* to compare them against the stored b-files.
<pre>
<nowiki>
#!make

# Generate OEIS A030707, A055187, A217760 and related
# "cumulative counting" sequences as defined by Clark Kimberling.
# http://faculty.evansville.edu/ck6/integer/unsolved.html, Problem 4
# @(#) $Id$
# 2018-04-20, Georg Fischer
#
# C.f. listing.tmp (produced by target "listing", below)
# Needs cumulcount.pl in current directory, and
# Unix tools diff, echo, grep, head, make, perl, sed, tee, test, wget
#---------------------------------
TARGET=cumulcount
LIMIT=100
P2=0

all: 0307io 0307do 05516n 05518n 2177nn
#----------
0307_list:
grep -aE "^A0307" ../names

0307io: 03070n 03071n 03072n 03073n 03074n
03070n: 030707 030708 030709 030710 030711 030712 030713 030714 030715 030716
03071n: 030717 030718 030719 030720 030721 030722 030723 030724 030725 030726
03072n: 030727 030728 030729 030730 030731 030732 030733 030734 030735 030736
03073n: 030737 030738 030739 030740 030741 030742 030743 030744 030745 030746
03074n: 030747 030748 030749 030750 030751 030752 030753 030754 030755 030756

0307do: 03075n 03076n 03077n 03078n
03075n: 030757 030758 030759 030760 030761 030762 030763 030764 030765 030766
03076n: 030767 030768 030769 030770 030771 030772 030773 030774 030775 030776
03077n: 030777 030778 030779 030780 030781 030782 030783 030784 030785 030786
03078n: 030787 030788 030789 030790 030791 030792 030793 030794 030795 030796

030707:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030708:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030709:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030710:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=io P1=1
030711:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030712:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030713:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=1
030714:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=2
030715:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=3
030716:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=4

030717:
make $(TARGET) RULE=A ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030718:
make $(TARGET) RULE=A ROW=4 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030719:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030720:
make $(TARGET) RULE=I ROW=3 NOEIS=$@ LEN=2000 ORD=io P1=1
030721:
make $(TARGET) RULE=J ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030722:
make $(TARGET) RULE=K ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
030723:
make $(TARGET) RULE=P ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=1
030724:
make $(TARGET) RULE=P ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=2
030725:
make $(TARGET) RULE=P ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=3
030726:
make $(TARGET) RULE=P ROW=3 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1 P2=4

030727:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3
030728:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3
030729:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3
030730:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=io P1=3
030731:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3
030732:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3
030733:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3 P2=1
030734:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3 P2=2
030735:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3 P2=3
030736:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=3 P2=4

030737:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2
030738:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2
030739:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2
030740:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=io P1=2
030741:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2
030742:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2
030743:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2 P2=1
030744:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2 P2=2
030745:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2 P2=3
030746:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=2 P2=4

030747:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4
030748:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4
030749:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4
030750:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=io P1=4
030751:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4
030752:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4
030753:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4 P2=1
030754:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4 P2=2
030755:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4 P2=3
030756:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=4 P2=4

030757:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1
030758:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1
030759:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1
030760:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=do P1=1
030761:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1
030762:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1
030763:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1 P2=1
030764:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1 P2=2
030765:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1 P2=3
030766:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=1 P2=4

030767:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2
030768:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2
030769:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2
030770:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=do P1=2
030771:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2
030772:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2
030773:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2 P2=1
030774:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2 P2=2
030775:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2 P2=3
030776:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=2 P2=4

030777:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3
030778:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3
030779:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3
030780:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=do P1=3
030781:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3
030782:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3
030783:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3 P2=1
030784:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3 P2=2
030785:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3 P2=3
030786:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=3 P2=4

030787:
make $(TARGET) RULE=A ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4
030788:
make $(TARGET) RULE=A ROW=2 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4
030789:
make $(TARGET) RULE=T ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4
030790:
make $(TARGET) RULE=I ROW=1 NOEIS=$@ LEN=2000 ORD=do P1=4
030791:
make $(TARGET) RULE=J ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4
030792:
make $(TARGET) RULE=K ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4
030793:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4 P2=1
030794:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4 P2=2
030795:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4 P2=3
030796:
make $(TARGET) RULE=P ROW=1 NOEIS=$@ LEN=$(LIMIT) ORD=do P1=4 P2=4

#----------
0551_list:
grep -aE "^A0551" ../names
05516n: 055168 055169 055170\
055171 055172 055173\
055174 055175 055176\
055177 055178 055179\
055180 055181 055182\
055183 055184 055185
055168:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=0
055169:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=0
055170:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=0
055171:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=1
055172:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=1
055173:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=1
055174:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=2
055175:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=2
055176:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=2
055177:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=3
055178:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=3
055179:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=3
055180:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=4
055181:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=4
055182:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=4
055183:
make $(TARGET) RULE=B ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=5
055184:
make $(TARGET) RULE=N ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=5
055185:
make $(TARGET) RULE=D ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=5
#-----
05518n: 055186 055187 \
055188 055189 055190 055191
055186:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=iz P1=0
055187:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=io P1=1
055188:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=2
055189:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=3
055190:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=4
055191:
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=$(LIMIT) ORD=fa P1=5
#----------
2177_list:
grep -aE "^A2177" ../names
2177nn: 217760 217780 # ok
217760: # c.f. 055186
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=10000 ORD=fa P1=0
217780: # c.f. 055187
make $(TARGET) RULE=A ROW=0 NOEIS=$@ LEN=10000 ORD=fa P1=1
#---------------------------------------------------------------
cumulcount:
# -------------------------------------------------------
test -s b$(NOEIS).txt || wget http://oeis.org/A$(NOEIS)/b$(NOEIS).txt
perl $(TARGET).pl $(RULE) $(ROW) $(NOEIS) $(LEN) $(ORD) $(P1) $(P2) > A$(NOEIS).pn.tmp
grep -E "^[0-9]" b$(NOEIS).txt | head -n $(LEN) > bf.tmp
grep -E "^[0-9]" A$(NOEIS).pn.tmp | head -n `wc -l bf.tmp | cut -d " " -f 1` > pn.tmp
# diff -w -y --width=32 bf.tmp pn.tmp || :
diff -w -y --suppress-common-lines --width=32 bf.tmp pn.tmp || :
#--------
list1:
echo [https://oeis.org/A$(NOEIS) A$(NOEIS)] Rule $(RULE).$(ROW) $(ORD) $(P1) $(P2) " "\
`wc -l b$(NOEIS).txt | cut -d " " -f 1`
listing:
make -s all TARGET=list1 | sort \
| sed -e "s/\.0/ /" -e "s/ 0 0/.0 /" -e "s/ 0/ /" -e "s/\.0/ 0/" \
| tee listing.tmp
wc -l listing.tmp
#----
</nowiki>
</pre>
== Results and Problems ==
The makefile currently generates and compares all 116 sequences in the list. Only a few problems were found:
# [https://oeis.org/A030717 A030717] (row 1) does not correspond with the derived sequences and [https://oeis.org/A030718 A030718] (row 2) and A030719-A030726. A030717 initially had no zero terms, but in 2014 the description was changed, and the b-file now has zero terms. This should be changed back.
* [https://oeis.org/A030740 A030740] (inverse) has a strange <code>Offset 2,1</code> which should be 1,1 IMHO as for the similiar [https://oeis.org/A030730 A030730], [https://oeis.org/A030750 A030750]. In the description there is a typo <code>j'2</code>.