A023429 - OEIS

%I #19 Jul 20 2021 19:00:13

%S 1,1,1,1,1,1,1,2,4,7,11,17,27,44,73,122,204,340,566,945,1586,2674,

%T 4521,7656,12982,22047,37509,63934,109166,186685,319679,548091,940819,

%U 1616830,2781706,4790949,8259748,14253480,24618561,42557378

%N Generalized Catalan Numbers.

%H Alois P. Heinz, <a href="/A023429/b023429.txt">Table of n, a(n) for n = 0..1000</a>

%F 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 a:= proc(n) option remember;

%p       `if`(n=0, 1, a(n-1) +add(a(k)*a(n-4-k), k=3..n-4))

%p     end:

%p seq(a(n), n=0..50);  # _Alois P. Heinz_, May 07 2011

%t 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 Cf. A000108, A001006, A004148, A006318.

%K nonn,easy

%O 0,8

%A _Olivier Gérard_