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A116754
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Number of permutations of length n which avoid the patterns 2134, 2143, 4312.
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1
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1, 2, 6, 21, 73, 239, 734, 2134, 5934, 15918, 41470, 105470, 262910, 644350, 1556478, 3713022, 8761342, 20475902, 47448062, 109117438, 249233406, 565772286, 1277165566, 2868379646, 6412042238, 14272167934, 31641829374, 69893881854, 153863847934, 337641471998
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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.: x*(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6) / ((1 - x)*(1 - 2*x)^4).
a(n) = (1/128)*(4*(-64 + 65*2^n) - 107*2^n*n + 9*2^(1+n)*n^2 + 2^n*n^3) for n > 2. - Colin Barker, Nov 02 2017
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MATHEMATICA
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CoefficientList[Series[(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6)/((1 - x)*(1 - 2*x)^4), {x, 0, 40}], x] (* Wesley Ivan Hurt, Dec 26 2023 *)
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PROG
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(PARI) Vec(x*(1 - 7*x + 20*x^2 - 25*x^3 + 12*x^4 - 2*x^5 - x^6) / ((1 - x)*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 02 2017
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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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