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
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).