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Number of Catalan words of length n avoiding the pattern 00000.
3

%I #8 Aug 25 2022 08:47:28

%S 1,1,2,5,14,41,125,389,1220,3829,12091,38237,120869,382000,1208863,

%T 3824981,12098811,38272739,121105815,383157721,1212151630,3835001361,

%U 12133807832,38388624860,121452176437,384255298818,1215726271065,3846304406380,12168956318213

%N Number of Catalan words of length n avoiding the pattern 00000.

%H Alois P. Heinz, <a href="/A356698/b356698.txt">Table of n, a(n) for n = 0..1000</a>

%H Jean-Luc Baril, Sergey Kirgizov and Vincent Vajnovszki, <a href="https://arxiv.org/abs/1803.06706">Descent distribution on Catalan words avoiding a pattern of length at most three</a>, arXiv:1803.06706 [math.CO], 2018.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,9,28,-37,-54,-37,25,10,-1)

%F 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).

%Y Cf. A000108, A307464, A356697.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Aug 23 2022