A356697 Number of Catalan words of length n avoiding the pattern 0000.

1, 1, 2, 5, 13, 36, 101, 280, 788, 2212, 6186, 17384, 48755, 136649, 383584, 1075734, 3016924, 8464693, 23740844, 66592246, 186807727, 523973400, 1469769653, 4122833303, 11564436141, 32438795011, 90992182917, 255234015580, 715941436278, 2008237780651

Offset

0,3

Links

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

Jean-Luc Baril, Sergey Kirgizov and Vincent Vajnovszki, Descent distribution on Catalan words avoiding a pattern of length at most three, arXiv:1803.06706 [math.CO], 2018.

Index entries for linear recurrences with constant coefficients, signature (1,3,9,-7,-6,1)

Formula

G.f.: -(3*x^5-9*x^3-2*x^2+1)/((x-1)*(x^5-5*x^4-12*x^3-3*x^2+1)).

Crossrefs

Cf. A000108, A307464, A356698.

Sequence in context: A331030 A046171 A022854 * A346738 A116409 A279196

Adjacent sequences: A356694 A356695 A356696 * A356698 A356699 A356700

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 23 2022

Status

approved