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 A096612 #7 May 09 2023 19:43:25
%S A096612 1,0,0,2,4,4,6,30,58,76,196,528,1010,1860,4470,10416,20762,43272,
%T A096612 99568,219198,457862,993192,2221840,4833382,10372864,22752468,
%U A096612 50238288,109413330,238079388,523375136,1150530568,2515127392,5508368758
%N A096612 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,n).
%C A096612 A diagonal of the array in A096608.
%H A096612 Paolo Xausa, <a href="/A096612/b096612.txt">Table of n, a(n) for n = 0..1000</a>
%t A096612 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 *)
%Y A096612 Cf. A096608, A096609, A096610, A096611.
%K A096612 nonn
%O A096612 0,4
%A A096612 _Clark Kimberling_, Jun 29 2004