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A363813
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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.
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4
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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
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OFFSET
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0,3
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COMMENTS
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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".
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LINKS
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FORMULA
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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).
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MATHEMATICA
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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 *)
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CROSSREFS
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Other entries including the patterns 1, 2, 3, 4 in the Merino and Mütze reference: A006318, A106228, A363809, A078482, A033321, A363810, A363811, A363812, A006012.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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