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%I #14 Apr 20 2023 18:14:32
%S 1,1,2,4,10,24,53,132,310,711,1736,4053,9475,22800,53294,125667,
%T 299629,702555,1661861,3941889,9269716,21941640,51908768,122325141,
%U 289466629,684020046,1614034607,3817513449,9017274205,21292938474,50340109313,118899240972
%N Expansion of x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).
%C Number of Catalan words of length n avoiding the pattern 1111 of length 4.
%H Mansour, Toufik; Shattuck, Mark <a href="https://doi.org/10.2298/FIL1703543M">Avoidance of classical patterns by Catalan sequences</a>. Filomat 31, No. 3, 543-558 (2017). Corollary 2.2
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,9,0,-3).
%F G.f.: x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).
%F a(n) = 2*a(n-2) + 9*a(n-3) - 3*a(n-5). - _Wesley Ivan Hurt_, Apr 20 2023
%Y Cf. A131572 (length 3).
%K nonn,easy
%O 1,3
%A _R. J. Mathar_, Aug 23 2022