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A096612
a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,n).
6
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 29 2004
STATUS
approved