A023429 Generalized Catalan Numbers.

1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 11, 17, 27, 44, 73, 122, 204, 340, 566, 945, 1586, 2674, 4521, 7656, 12982, 22047, 37509, 63934, 109166, 186685, 319679, 548091, 940819, 1616830, 2781706, 4790949, 8259748, 14253480, 24618561, 42557378

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

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

Maple

a:= proc(n) option remember;
      `if`(n=0, 1, a(n-1) +add(a(k)*a(n-4-k), k=3..n-4))
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, May 07 2011

Mathematica

Clear[ a ]; a[ 0 ]=1; a[ n_Integer ] := a[ n ]=a[ n-1 ]+Sum[ a[ k ]*a[ n-4-k ], {k, 3, n-4} ];

Crossrefs

Cf. A000108, A001006, A004148, A006318.

Sequence in context: A006999 A005252 A023430 * A023428 A093911 A152398

Adjacent sequences: A023426 A023427 A023428 * A023430 A023431 A023432

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved