OEIS/Triangles - Revision history

imported>Gfis: more comments

2018-03-18T09:07:06Z

more comments

← Older revision		Revision as of 09:07, 18 March 2018
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	0 3 7 9 0 3 6 9 0 3 7 9 0 2 7 9		0 3 7 9 0 3 6 9 0 3 7 9 0 2 7 9
	- R. H. Hardin, Jul 06 2012		- R. H. Hardin, Jul 06 2012
	* [https://oeis.org/A231074 A231074] The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order.		* [https://oeis.org/A231074 A231074] The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order: 1, 1, 1, 1, 2, 12, 244. nonn,more. Vladimir Letsko, [http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183 Mathematical Marathon, Problem 183] (in Russian)
	1, 1, 1, 1, 2, 12, 244		* [https://oeis.org/A231085 A231085] The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in increasing order provided that all sums are different: 1, 1, 1, 1, 2, 12, 168, 4676. nonn,more. Vladimir Letsko, Mathematical Marathon, Problem 183 (in Russian). For n<=5, a(n) = A231074(n), but for n>5, a(n) < A231074(n). For instance, let n = 6 and a < b < c < d < e < f. Then the arrangement a+b <= a+c <= a+d <= a+e <= b+c <= b+d <= a+f <= b+e <= b+f <= c+d <= c+e <= c+f <= d+e <= d+f <= e+f is possible (e.g., for a = 1, b = 5, c = 9, d = 12, e=13, f = 16), while the same arrangement with "<" instead of "<=" is not possible.
	nonn,more		* [https://oeis.org/A131811 A131811] Number of symbolic sequences on n symbols that can be realized by the arrangement of the real roots of some polynomial of degree n and its derivatives: 1, 1, 2, 10, 116. nonn,hard,more
	: Vladimir Letsko, [http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183 Mathematical Marathon, Problem 183] (in Russian)		* [https://oeis.org/A213457 A213457] Intertwining numbers. (Formerly M1988): 1, 1, 2, 10, 148, 7384, 1380960, more. a(4)=10 for example is the number of ways of arranging 1 a, 2 b's, 3 c's and 4 d's so that if we look at any two letters, i and j say, with i<j, then any pair of i's are separated by at least one j.
	* [https://oeis.org/A231085 A231085] ~~similiar~~, ~~same author:~~ a(1..7), ~~more~~
	* [https://oeis.org/A131811 A131811] Number of symbolic sequences on n symbols that can be realized by the arrangement of the real roots of some polynomial of degree n and its derivatives.
	* [https://oeis.org/A213457 A213457] Intertwining numbers. (Formerly M1988)
	1, 1, 2, 10, 148, 7384, 1380960, more
	* [https://oeis.org/A083568 A083568] Duplicate of A003121. dead		* [https://oeis.org/A083568 A083568] Duplicate of A003121. dead

imported>Gfis: +dead A083568

2018-03-17T13:54:34Z

+dead A083568

← Older revision		Revision as of 13:54, 17 March 2018
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	1, 1, 1, 1, 2, 12, 244		1, 1, 1, 1, 2, 12, 244
	nonn,more		nonn,more
	: Vladimir Letsko, [http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183 Mathematical Marathon, Problem 183] (in Russian)		: Vladimir Letsko, [http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183 Mathematical Marathon, Problem 183] (in Russian)
			* [https://oeis.org/A231085 A231085] similiar, same author: a(1..7), more
	* [https://oeis.org/A131811 A131811] Number of symbolic sequences on n symbols that can be realized by the arrangement of the real roots of some polynomial of degree n and its derivatives.		* [https://oeis.org/A131811 A131811] Number of symbolic sequences on n symbols that can be realized by the arrangement of the real roots of some polynomial of degree n and its derivatives.
			* [https://oeis.org/A213457 A213457] Intertwining numbers. (Formerly M1988)
			1, 1, 2, 10, 148, 7384, 1380960, more
			* [https://oeis.org/A083568 A083568] Duplicate of A003121. dead

imported>Gfis: A231074 etc.

2018-03-17T13:42:08Z

A231074 etc.

← Older revision		Revision as of 13:42, 17 March 2018
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	* [https://oeis.org/A282698/b282698.txt A282698] contains A003121 (for triangles with strict "less than" interlacing), and 20, 1744		* [https://oeis.org/A282698/b282698.txt A282698] contains A003121 (for triangles with strict "less than" interlacing), and 20, 1744
	* [https://oeis.org/A003121 A003121]		* [https://oeis.org/A003121 A003121]
			Number of ways to arrange the numbers 1,2,...,n(n+1)/2
			in a triangle so that the rows interlace;
			e.g. one of the 12 triangles counted by a(4) is
			6
			4 8
			2 5 9
			1 3 7 10
			- Clark Kimberling, Mar 25 2012
			The a(4) = 12 ways to fill a triangle with the numbers 0 through 9:
			5 6 6 5
			3 7 3 7 2 7 2 7
			1 4 8 1 4 8 1 4 8 1 4 8
			0 2 6 9 0 2 5 9 0 3 5 9 0 3 6 9
			5 3 3 4
			3 6 2 6 2 7 3 7
			1 4 8 1 5 8 1 5 8 1 5 8
			0 2 7 9 0 4 7 9 0 4 6 9 0 2 6 9
			4 4 5 4
			2 6 2 7 2 6 3 6
			1 5 8 1 5 8 1 4 8 1 5 8
			0 3 7 9 0 3 6 9 0 3 7 9 0 2 7 9
			- R. H. Hardin, Jul 06 2012
			* [https://oeis.org/A231074 A231074] The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order.
			1, 1, 1, 1, 2, 12, 244
			nonn,more
			: Vladimir Letsko, [http://www-old.fizmat.vspu.ru/doku.php?id=marathon:problem_183 Mathematical Marathon, Problem 183] (in Russian)
			* [https://oeis.org/A131811 A131811] Number of symbolic sequences on n symbols that can be realized by the arrangement of the real roots of some polynomial of degree n and its derivatives.

imported>Gfis: Created page with "* [https://oeis.org/A282698/b282698.txt A282698] contains A003121 (for triangles with strict "less than" interlacing), and 20, 1744 * [https://oeis.org/A003121 A003121]"

2018-03-15T21:09:05Z

Created page with "* [https://oeis.org/A282698/b282698.txt A282698] contains A003121 (for triangles with strict "less than" interlacing), and 20, 1744 * [https://oeis.org/A003121 A003121]"

New page

* [https://oeis.org/A282698/b282698.txt A282698] contains A003121 (for triangles with strict "less than" interlacing), and 20, 1744
* [https://oeis.org/A003121 A003121]