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A116771
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Number of permutations of length n which avoid the patterns 1243, 4132, 4321.
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0
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1, 2, 6, 21, 74, 237, 668, 1667, 3750, 7743, 14898, 27033, 46698, 77369, 123672, 191639, 288998, 425499, 613278, 867261, 1205610, 1650213, 2227220, 2967627, 3907910, 5090711, 6565578, 8389761, 10629066, 13358769
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: A(x) = -{(x^9-3x^8+3x^7-4x^6+19x^5-32x^4+27x^3-18x^2+6x-1)x}/{(x-1)^8}
For n >= 4, a(n) = (5n^6 - 84n^5 + 860n^4 - 5610n^3 + 22535n^2 - 49566n + 45900)/180. - Franklin T. Adams-Watters, Sep 16 2006
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MATHEMATICA
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LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 6, 21, 74, 237, 668, 1667, 3750, 7743}, 30] (* Harvey P. Dale, Mar 30 2024 *)
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CROSSREFS
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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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