OFFSET
0,3
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Jean-Luc Baril and José L. Ramírez, Knight's paths towards Catalan numbers, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087, Jan 2023.
FORMULA
Row sums of array in A096587.
EXAMPLE
Rows of array T(n,k) in A096587:
1
0 0 1
1 1 0 0 1
0 1 2 2 0 0 1
...
so a(3)=T(3,0)+T(3,1)+...+T(3,6)=6.
MATHEMATICA
A096588list[nmax_]:=Module[{T}, T[0, 0]=1; T[n_, k_]:=T[n, k]=If[0<=k<=2n, T[n-1, k-2]+T[n-2, k-1]+T[n-1, k+2]+T[n-2, k+1], 0]; Table[Sum[T[n, k], {k, 0, 2n}], {n, 0, nmax}]]; A096588list[50] (* Paolo Xausa, May 22 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 28 2004.
STATUS
approved