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 A363809 #14 Jan 16 2024 17:31:57 %S A363809 1,1,2,6,22,89,378,1647,7286,32574,146866,667088,3050619,14039075, %T A363809 64992280,302546718,1415691181,6656285609,31436228056,149079962872, %U A363809 709680131574,3390269807364,16248661836019,78109838535141,376531187219762,1819760165454501 %N A363809 Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, and 2-1-3-5-4. %C A363809 Equivalently, for n>0, the number of separable permutations of [n] that avoid 2-1-3-5-4. %C A363809 The number of guillotine rectangulations (with respect to the weak equivalence) that avoid the geometric pattern "7". See the Merino and Mütze reference, Table 3, entry "12347". %D A363809 Andrei Asinowski and Cyril Banderier. Geometry meets generating functions: Rectangulations and permutations (2023). %H A363809 Andrei Asinowski and Cyril Banderier, <a href="https://arxiv.org/abs/2401.05558">From geometry to generating functions: rectangulations and permutations</a>, arXiv:2401.05558 [cs.DM], 2024. See page 2. %H A363809 Arturo Merino and Torsten Mütze. <a href="https://doi.org/10.1007/s00454-022-00393-w">Combinatorial generation via permutation languages. III. Rectangulations</a>. Discrete & Computational Geometry, 70 (2023), 51-122. Preprint: arXiv:2103.09333 [math.CO], 2021. %F A363809 The generating function F=F(x) satisfies the equation x^4*(x - 2)^2*F^4 + x*(x - 2)*(4*x^3 - 7*x^2 + 6*x - 1)*F^3 + (2*x^4 - x^3 - 2*x^2 + 5*x - 1)*F^2 - (4*x^3 - 7*x^2 + 6*x - 1)*F + x^2 = 0. %Y A363809 Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A078482, A033321, A363810, A363811, A363812, A363813, A006012. %K A363809 nonn %O A363809 0,3 %A A363809 _Andrei Asinowski_, Jun 23 2023