%I #8 May 09 2023 18:40:03

%S 1,0,2,0,8,6,44,60,256,460,1582,3360,10324,24150,69652,172200,479728,

%T 1225308,3350972,8727312,23638174,62295420,167923252,445808220,

%U 1199180360,3198756132,8598547622,23009417080,61856381708,165897510350

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

%C Column 0 of the array in A096608.

%H Paolo Xausa, <a href="/A096609/b096609.txt">Table of n, a(n) for n = 0..1000</a>

%t A096609[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,0],{n,0,nmax}]];A096609[50] (* _Paolo Xausa_, May 09 2023 *)

%Y Cf. A096608, A096610, A096611, A096612.

%K nonn

%O 0,3

%A _Clark Kimberling_, Jun 29 2004