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A263790
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The number of length-n permutations avoiding the patterns 1234, 1324 and 2143.
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1
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1, 1, 2, 6, 21, 75, 268, 958, 3425, 12245, 43778, 156514, 559565, 2000543, 7152292, 25570698, 91419729, 326841561, 1168515890, 4177649198, 14935828405, 53398205443, 190907947468, 682529386598, 2440162233937, 8724007852045, 31189857766034, 111509210441322, 398664979703373
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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*x^3 + 3*x - 1)/(-x^4 + 2*x^3 - 2*x^2 + 4*x - 1).
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MAPLE
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t1:=(1-3*x-2*x^3)/(1-4*x+2*x^2-2*x^3+x^4);
series(t1, x, 40);
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MATHEMATICA
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CoefficientList[Series[(2 x^3 + 3 x - 1)/(-x^4 + 2*x^3 - 2 x^2 + 4 x - 1), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 01 2016 *)
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PROG
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(PARI) Vec((2*x^3 + 3*x - 1)/(-x^4 + 2*x^3 - 2*x^2 + 4*x - 1) + O(x^50)) \\ Michel Marcus, Nov 23 2015
(Magma) I:=[1, 1, 2, 6]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jan 01 2016
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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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