A096612 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,n).

1, 0, 0, 2, 4, 4, 6, 30, 58, 76, 196, 528, 1010, 1860, 4470, 10416, 20762, 43272, 99568, 219198, 457862, 993192, 2221840, 4833382, 10372864, 22752468, 50238288, 109413330, 238079388, 523375136, 1150530568, 2515127392, 5508368758

Offset

0,4

Comments

A diagonal of the array in A096608.

Links

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

Mathematica

A096612[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, n], {n, 0, nmax}]]; A096612[50] (* Paolo Xausa, May 09 2023 *)

Crossrefs

Cf. A096608, A096609, A096610, A096611.

Sequence in context: A159788 A179112 A359119 * A218707 A177153 A164719

Adjacent sequences: A096609 A096610 A096611 * A096613 A096614 A096615

Keyword

nonn

Author

Clark Kimberling, Jun 29 2004

Status

approved