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A363812
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Number of permutations of [n] that avoid the patterns 2-41-3, 3-14-2, 2-1-4-3, and 3-41-2.
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4
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1, 1, 2, 6, 20, 69, 243, 870, 3159, 11611, 43130, 161691, 611065, 2325739, 8907360, 34304298, 132770564, 516164832, 2014739748, 7892775473, 31022627947, 122304167437, 483513636064, 1916394053725, 7613498804405, 30313164090695
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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 3-41-2.
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".
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LINKS
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FORMULA
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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)).
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MATHEMATICA
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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 *)
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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, A363813, 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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