OEIS/Coordination sequences for lattices - Revision history

imported>Gfis at 14:45, 28 July 2020

2020-07-28T14:45:28Z

@@ Line 10: / Line 10: @@
   [1, 16, 36, 16, 1]
 === A*_n ===
-* [https://oeis.org/A204621] coordinator triangle, rows are the g.f.s numerator coefficients
+* [https://oeis.org/A204621 A204621] coordinator triangle, rows are the g.f.s numerator coefficients
 * [https://oeis.org/A008535 A008535 (A*_7)]
   d:=7; CoefficientList[Series[((Sum[Sum[Binomial[d+1, j], {j,0,Min[k,d-k]}]*x^k, {k,0,d}])/(1-x)^d),{x,0,10}],x]
@@ Line 26: / Line 26: @@
   n:=4; f:= gfun:-rectoproc({a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1),a(0)=1},a(k),remember): map(f, [$0..n]);
   [1, 28, 70, 28, 1]

imported>Gfis: A.

2020-07-28T14:18:57Z

@@ Line 1: / Line 1: @@
-The recurrences were derived by Mathematica:
+The recurrences were derived by Mathematica. Auxilliary function:
   bin[n_,k_]:=(n!/(n-k)!/k!);
 === C_n ===
@@ Line 7: / Line 24: @@
   {1, 32, 192, 608, 1408, 2720, 4672, 7392, 11008, 15648, 21440, 28512}
   InputForm[FullSimplify[bin[2*n,2*k]/bin[2*n,2*k-2]]] -> ((-1 + 2*k - 2*n)*(-1 + k - n))/(k*(-1 + 2*k))
-  n:=4; f:= gfun:-rectoproc({a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1),a(0)=1},a(k),remember): map(f, [$0
+  n:=4; f:= gfun:-rectoproc({a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1),a(0)=1},a(k),remember): map(f, [$0..n]);
-   Recurrence: a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1), a(0)=1, k=0..n
+ [1, 28, 70, 28, 1]

imported>Gfis: Created page with "The recurrences were derived by Mathematica: bin[n_,k_]:=(n!/(n-k)!/k!); === C_n === * [https://oeis.org/A103884 A103884 (C_4)] d:= 4; CoefficientList[Series[(Sum[Binomial[..."

2020-07-28T13:50:26Z

Created page with "The recurrences were derived by Mathematica: bin[n_,k_]:=(n!/(n-k)!/k!); === C_n === * [https://oeis.org/A103884 A103884 (C_4)] d:= 4; CoefficientList[Series[(Sum[Binomial[..."

New page

The recurrences were derived by Mathematica:
bin[n_,k_]:=(n!/(n-k)!/k!);

=== C_n ===
* [https://oeis.org/A103884 A103884 (C_4)]
d:= 4; CoefficientList[Series[(Sum[Binomial[2n,2k]*x^k, {k, 0, d}])/(1-x)^d, {x,0,11}],x]
{1, 32, 192, 608, 1408, 2720, 4672, 7392, 11008, 15648, 21440, 28512}
InputForm[FullSimplify[bin[2*n,2*k]/bin[2*n,2*k-2]]] -> ((-1 + 2*k - 2*n)*(-1 + k - n))/(k*(-1 + 2*k))
n:=4; f:= gfun:-rectoproc({a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1),a(0)=1},a(k),remember): map(f, [$0
Recurrence: a(k)=(2*n-2*k+1)*(n-(k-1))/(k*(2*k-1))*a(k-1), a(0)=1, k=0..n