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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.
4
1, 1, 2, 6, 21, 78, 295, 1114, 4166, 15390, 56167, 202738, 724813, 2570276, 9052494, 31702340, 110503497, 383691578, 1328039043, 4584708230, 15793983638, 54315199642, 186526735307, 639831906594, 2192754259993, 7509139583560, 25699765092254, 87913948206096
OFFSET
0,3
COMMENTS
Equivalently, for n>0, the number of separable permutations of [n] that avoid 2-1-4-3 and 4-5-3-1-2.
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".
LINKS
Andrei Asinowski and Cyril Banderier, From geometry to generating functions: rectangulations and permutations, arXiv:2401.05558 [cs.DM], 2024. See page 2.
Arturo Merino and Torsten Mütze. Combinatorial generation via permutation languages. III. Rectangulations. Discrete & Computational Geometry, 70 (2023), 51-122. Preprint: arXiv:2103.09333 [math.CO], 2021.
FORMULA
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).
MATHEMATICA
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 *)
CROSSREFS
Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A363809, A078482, A033321, A363810, A363811, A363812, A006012.
Sequence in context: A150189 A144169 A355152 * A124292 A277221 A360168
KEYWORD
nonn,easy
AUTHOR
Andrei Asinowski, Jun 23 2023
STATUS
approved