cp's OEIS Frontend

A363813 Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, 2-1-4-3, and 4-5-3-1-2.

%I A363813 #21 Jan 16 2024 17:21:03
%S A363813 1,1,2,6,21,78,295,1114,4166,15390,56167,202738,724813,2570276,
%T A363813 9052494,31702340,110503497,383691578,1328039043,4584708230,
%U A363813 15793983638,54315199642,186526735307,639831906594,2192754259993,7509139583560,25699765092254,87913948206096
%N A363813 Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, 2-1-4-3, and 4-5-3-1-2.
%C A363813 Equivalently, for n>0, the number of separable permutations of [n] that avoid 2-1-4-3 and 4-5-3-1-2.
%C A363813 The number of guillotine rectangulations (with respect to the weak equivalence) that avoid the geometric patterns "5", "7", "8". See the Merino and Mütze reference, Table 3, entry "1234578".
%H A363813 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 A363813 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.
%H A363813 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-37,62,-47,16,-2).
%F A363813 G.f.: (1 - 9*x + 29*x^2 - 39*x^3 + 20*x^4 - 3*x^5)/((1 - 4*x + 2*x^2)*(1 - 3*x + x^2)^2).
%t A363813 CoefficientList[Series[(1 - 9*x + 29*x^2 - 39*x^3 + 20*x^4 - 3*x^5)/((1 - 4*x + 2*x^2)*(1 - 3*x + x^2)^2),{x,0,27}],x] (* _Stefano Spezia_, Jun 24 2023 *)
%Y A363813 Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A363809, A078482, A033321, A363810, A363811, A363812, A006012.
%K A363813 nonn,easy
%O A363813 0,3
%A A363813 _Andrei Asinowski_, Jun 23 2023