A356698 Number of Catalan words of length n avoiding the pattern 00000.

1, 1, 2, 5, 14, 41, 125, 389, 1220, 3829, 12091, 38237, 120869, 382000, 1208863, 3824981, 12098811, 38272739, 121105815, 383157721, 1212151630, 3835001361, 12133807832, 38388624860, 121452176437, 384255298818, 1215726271065, 3846304406380, 12168956318213

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 (1,3,9,28,-37,-54,-37,25,10,-1)

Formula

G.f.: -(4*x^9-40*x^7-32*x^6-3*x^5+34*x^4+9*x^3+2*x^2-1) / (x^10 -10*x^9 -25*x^8 +37*x^7 +54*x^6 +37*x^5 -28*x^4 -9*x^3 -3*x^2 -x +1).

Crossrefs

Cf. A000108, A307464, A356697.

Sequence in context: A159771 A159768 A128739 * A036766 A366024 A222589

Adjacent sequences: A356695 A356696 A356697 * A356699 A356700 A356701

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 23 2022

Status

approved