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 A096610 #7 May 09 2023 18:40:26
%S A096610 0,0,1,2,6,12,33,76,210,520,1410,3590,9618,24920,66521,174412,465264,
%T A096610 1229184,3280458,8710668,23271116,62014876,165888184,443255164,
%U A096610 1187255082,3178905184,8525398102,22864654046,61391533270,164872981784
%N A096610 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,1).
%C A096610 Column 1 of the array in A096608.
%H A096610 Paolo Xausa, <a href="/A096610/b096610.txt">Table of n, a(n) for n = 0..1000</a>
%t A096610 A096610[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,1],{n,0,nmax}]];A096610[50] (* _Paolo Xausa_, May 09 2023 *)
%Y A096610 Cf. A096608, A096609, A096611, A096612.
%K A096610 nonn
%O A096610 0,4
%A A096610 _Clark Kimberling_, Jun 29 2004