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

Author

Clark Kimberling, Jun 29 2004

Keywords

• nonn

Comments

Column 1 of the array in A096608.

Links

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

Crossrefs

Cf. A096608, A096609, A096611, A096612.

Programs

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 *)