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A165532
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Number of permutations of length n which avoid the patterns 4231 and 3214.
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1
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1, 1, 2, 6, 22, 87, 352, 1428, 5768, 23156, 92416, 367007, 1451780, 5725959, 22535868, 88566290, 347742688, 1364637732, 5353992916, 21005649217, 82425637860, 323523434437, 1270281675368, 4989615315114, 19607400037358, 77084254889327, 303184014866196, 1193001145648675
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (2 - 13*x + 26*x^2 - 17*x^3 + 4*x^4 - x*(1 - 2*x - x^2)*sqrt(1 - 4*x))/(2*sqrt(1 - 4*x)*(1 - 3*x + x^2)^2). - G. C. Greubel, Oct 22 2018
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EXAMPLE
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There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
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MATHEMATICA
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CoefficientList[Series[(2 - 13*x + 26*x^2 - 17*x^3 + 4*x^4 - x*(1 - 2*x - x^2)*Sqrt[1 - 4*x])/(2*Sqrt[1 - 4*x]*(1 - 3*x + x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 22 2018 *)
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PROG
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(PARI) x='x+O('x^50); Vec((2 - 13*x + 26*x^2 - 17*x^3 + 4*x^4 - x*(1 - 2*x - x^2)*sqrt(1 - 4*x))/(2*sqrt(1 - 4*x)*(1 - 3*x + x^2)^2)) \\ G. C. Greubel, Oct 22 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((2 - 13*x + 26*x^2 - 17*x^3 + 4*x^4 - x*(1 - 2*x - x^2)*Sqrt(1 - 4*x))/( 2*Sqrt(1 - 4*x)*(1 - 3*x + x^2)^2))); // G. C. Greubel, Oct 22 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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