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 A096611 #7 May 09 2023 19:03:25
%S A096611 0,1,0,3,1,16,18,95,154,581,1160,3752,8485,25208,61180,173343,438242,
%T A096611 1210222,3134472,8538629,22437042,60690510,160889234,433701996,
%U A096611 1156122902,3112018729,8325803356,22402792752,60084101129,161701735578
%N A096611 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,2).
%C A096611 Column 2 of the array in A096608.
%H A096611 Paolo Xausa, <a href="/A096611/b096611.txt">Table of n, a(n) for n = 0..1000</a>
%t A096611 A096611[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,2],{n,0,nmax}]];A096611[50] (* _Paolo Xausa_, May 09 2023 *)
%Y A096611 Cf. A096608, A096609, A096610, A096612.
%K A096611 nonn
%O A096611 0,4
%A A096611 _Clark Kimberling_, Jun 29 2004