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 A116713 Number of permutations of length n which avoid the patterns 123, 2431, 4132. 1
 1, 2, 5, 12, 24, 45, 83, 154, 290, 555, 1077, 2112, 4172, 8281, 16487, 32886, 65670, 131223, 262313, 524476, 1048784, 2097381, 4194555, 8388882, 16777514, 33554755, 67109213, 134218104, 268435860, 536871345, 1073742287, 2147484142, 4294967822, 8589935151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005. Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA G.f.: x*(1 - 3*x + 4*x^2 - 2*x^3 - 3*x^4 + 2*x^5) / ((1 - x)^3*(1 - 2*x)). From Colin Barker, Oct 19 2017: (Start) a(n) = (-4 + 2^n - n + n^2) / 2 for n>2. a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>6. (End) MAPLE A116713 := proc(n) coeftayl(x*(2*x^5-3*x^4-2*x^3+4*x^2-3*x+1)/(x-1)^3/(2*x-1), x=0, n) ; end: seq(A116713(n), n=1..50) ; # R. J. Mathar, Jan 23 2008 PROG (PARI) Vec(x*(1 - 3*x + 4*x^2 - 2*x^3 - 3*x^4 + 2*x^5) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Oct 19 2017 CROSSREFS Sequence in context: A116721 A294868 A192981 * A261369 A116714 A023615 Adjacent sequences: A116710 A116711 A116712 * A116714 A116715 A116716 KEYWORD nonn,easy AUTHOR Lara Pudwell, Feb 26 2006 STATUS approved

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Last modified September 13 10:14 EDT 2024. Contains 375904 sequences. (Running on oeis4.)