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A356698
Number of Catalan words of length n avoiding the pattern 00000.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 23 2022
STATUS
approved