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Number of Catalan words of length n avoiding the pattern 0000.
3

%I #9 Aug 25 2022 08:49:11

%S 1,1,2,5,13,36,101,280,788,2212,6186,17384,48755,136649,383584,

%T 1075734,3016924,8464693,23740844,66592246,186807727,523973400,

%U 1469769653,4122833303,11564436141,32438795011,90992182917,255234015580,715941436278,2008237780651

%N Number of Catalan words of length n avoiding the pattern 0000.

%H Alois P. Heinz, <a href="/A356697/b356697.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,9,-7,-6,1)

%F 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)).

%Y Cf. A000108, A307464, A356698.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Aug 23 2022