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 A363812 #20 Jan 16 2024 17:31:53
%S A363812 1,1,2,6,20,69,243,870,3159,11611,43130,161691,611065,2325739,8907360,
%T A363812 34304298,132770564,516164832,2014739748,7892775473,31022627947,
%U A363812 122304167437,483513636064,1916394053725,7613498804405,30313164090695
%N A363812 Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, 2-1-4-3, and 3-41-2.
%C A363812 Equivalently, for n>0, the number of separable permutations of [n] that avoid 2-1-4-3 and 3-41-2.
%C A363812 The number of guillotine rectangulations (with respect to the weak equivalence) that avoid the geometric patterns "5", "6", "7". See the Merino and Mütze reference, Table 3, entry "1234567".
%H A363812 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 A363812 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 A363812 G.f.: (1 - 3*x + 3*x^2 - sqrt(1 - 6*x + 7*x^2 + 2*x^3 + x^4))/(2*x^2*(2 - x)).
%t A363812 CoefficientList[Series[(1 - 3*x + 3*x^2 - Sqrt[1 - 6*x + 7*x^2 + 2*x^3 + x^4])/(2*x^2*(2 - x)),{x,0,25}],x] (* _Stefano Spezia_, Jun 24 2023 *)
%Y A363812 Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A363809, A078482, A033321, A363810, A363811, A363813, A006012.
%K A363812 nonn,easy
%O A363812 0,3
%A A363812 _Andrei Asinowski_, Jun 23 2023