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A165527
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Number of permutations of length n which avoid the patterns 4231 and 2143.
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1
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1, 2, 6, 22, 86, 335, 1271, 4680, 16766, 58656, 201106, 677767, 2251011, 7382992, 23955716, 77010180, 245577076, 777648145, 2447486221, 7661760386, 23872087936, 74071120682, 228988898916, 705618033237, 2168073549821, 6644571015750, 20317533778906
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OFFSET
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1,2
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REFERENCES
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Kremer, Darla; and Shiu, Wai Chee; Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268 (2003), no. 1-3, 171-183. MR1983276 (2004b:05006). See Table 1.
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LINKS
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FORMULA
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G.f.: (x-11*x^2+51*x^3-127*x^4+186*x^5-165*x^6+87*x^7-23*x^8+3*x^9) / ((1-3*x)*(1-x)^4*(1-3*x+x^2)^2). - Vincent Vatter, Jun 21 2011
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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[(x-11*x^2+51*x^3-127*x^4+186*x^5-165*x^6+87*x^7 -23*x^8+3*x^9)/((1-3*x)*(1-x)^4*(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) Vec(x*(1 - 11*x + 51*x^2 - 127*x^3 + 186*x^4 - 165*x^5 + 87*x^6 - 23*x^7 + 3*x^8) / ((1 - x)^4*(1 - 3*x)*(1 - 3*x + x^2)^2) + O(x^30)) \\ Colin Barker, Oct 31 2017
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x -11*x^2+51*x^3-127*x^4+186*x^5-165*x^6+87*x^7 -23*x^8+3*x^9)/((1-3*x)* (1-x)^4*(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,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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