This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356695 #14 Apr 20 2023 18:14:32 %S A356695 1,1,2,4,10,24,53,132,310,711,1736,4053,9475,22800,53294,125667, %T A356695 299629,702555,1661861,3941889,9269716,21941640,51908768,122325141, %U A356695 289466629,684020046,1614034607,3817513449,9017274205,21292938474,50340109313,118899240972 %N A356695 Expansion of x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5). %C A356695 Number of Catalan words of length n avoiding the pattern 1111 of length 4. %H A356695 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 A356695 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,9,0,-3). %F A356695 G.f.: x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5). %F A356695 a(n) = 2*a(n-2) + 9*a(n-3) - 3*a(n-5). - _Wesley Ivan Hurt_, Apr 20 2023 %Y A356695 Cf. A131572 (length 3). %K A356695 nonn,easy %O A356695 1,3 %A A356695 _R. J. Mathar_, Aug 23 2022