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 A023429 #22 Feb 03 2025 09:36:43
%S A023429 1,1,1,1,1,1,1,2,4,7,11,17,27,44,73,122,204,340,566,945,1586,2674,
%T A023429 4521,7656,12982,22047,37509,63934,109166,186685,319679,548091,940819,
%U A023429 1616830,2781706,4790949,8259748,14253480,24618561,42557378
%N A023429 Generalized Catalan Numbers x^4*A(x)^2 -(1-x+x^4+x^5+x^6)*A(x) + 1 =0.
%H A023429 Alois P. Heinz, <a href="/A023429/b023429.txt">Table of n, a(n) for n = 0..1000</a>
%F A023429 G.f. A(x) satisfies: A(x) = (1 + x^4 * A(x)^2) / (1 - x + x^4 + x^5 + x^6). - _Ilya Gutkovskiy_, Jul 20 2021
%p A023429 a:= proc(n) option remember;
%p A023429 `if`(n=0, 1, a(n-1) +add(a(k)*a(n-4-k), k=3..n-4))
%p A023429 end:
%p A023429 seq(a(n), n=0..50); # _Alois P. Heinz_, May 07 2011
%t A023429 Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 3, n-4} ];
%Y A023429 Cf. A000108, A001006, A004148, A006318.
%K A023429 nonn,easy
%O A023429 0,8
%A A023429 _Olivier Gérard_