A096610 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,1).

0, 0, 1, 2, 6, 12, 33, 76, 210, 520, 1410, 3590, 9618, 24920, 66521, 174412, 465264, 1229184, 3280458, 8710668, 23271116, 62014876, 165888184, 443255164, 1187255082, 3178905184, 8525398102, 22864654046, 61391533270, 164872981784

Offset

0,4

Comments

Column 1 of the array in A096608.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Mathematica

A096610[nmax_]:=Module[{T}, T[0, 0]=1; T[n_, k_]:=T[n, k]=If[k<=2n, T[n-1, Abs[k-2]]+T[n-2, Abs[k-1]]+T[n-1, k+2]+T[n-2, k+1], 0]; Table[T[n, 1], {n, 0, nmax}]]; A096610[50] (* Paolo Xausa, May 09 2023 *)

Crossrefs

Cf. A096608, A096609, A096611, A096612.

Sequence in context: A360867 A217447 A057579 * A164099 A088808 A076278

Adjacent sequences: A096607 A096608 A096609 * A096611 A096612 A096613

Keyword

nonn

Author

Clark Kimberling, Jun 29 2004

Status

approved