This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096609 #8 May 09 2023 18:40:03
%S A096609 1,0,2,0,8,6,44,60,256,460,1582,3360,10324,24150,69652,172200,479728,
%T A096609 1225308,3350972,8727312,23638174,62295420,167923252,445808220,
%U A096609 1199180360,3198756132,8598547622,23009417080,61856381708,165897510350
%N A096609 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,0).
%C A096609 Column 0 of the array in A096608.
%H A096609 Paolo Xausa, <a href="/A096609/b096609.txt">Table of n, a(n) for n = 0..1000</a>
%t A096609 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 A096609 Cf. A096608, A096610, A096611, A096612.
%K A096609 nonn
%O A096609 0,3
%A A096609 _Clark Kimberling_, Jun 29 2004