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 A116699 Number of permutations of length n which avoid the patterns 123 and 4312. 7
 1, 2, 5, 13, 30, 61, 112, 190, 303, 460, 671, 947, 1300, 1743, 2290, 2956, 3757, 4710, 5833, 7145, 8666, 10417, 12420, 14698, 17275, 20176, 23427, 27055, 31088, 35555, 40486, 45912, 51865, 58378, 65485, 73221, 81622, 90725, 100568, 111190, 122631, 134932 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also number of permutations of length n which avoid the patterns 321, 2134 (reverse symmetry); or 321, 1243 (complement symmetry); etc. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017. Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: x*(2*x^3 - 5*x^2 + 3*x - 1)/(x-1)^5. a(n) = (n^4 + 2*n^3 - 13*n^2 + 34*n)/24. - Franklin T. Adams-Watters, Sep 16 2006 Partial sums of A105163. - Levi R. Self (levi.r.self(AT)gmail.com), Aug 04 2007 Binomial transform of [1, 1, 2, 3, 1, 0, 0, 0, ...]. - Gary W. Adamson, Oct 23 2007 MATHEMATICA LinearRecurrence[{5, -10, 10, -5, 1}, {1, 2, 5, 13, 30}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *) CoefficientList[Series[(2 x^3 - 5 x^2 + 3 x - 1)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 01 2014 *) PROG (PARI) for(n=1, 100, print1((n^4 + 2*n^3 - 13*n^2 + 34*n)/24", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008 (Magma) [(n^4 + 2*n^3 - 13*n^2 + 34*n)/24: n in [1..45]]; // Vincenzo Librandi, Nov 01 2014 CROSSREFS Sequence in context: A122025 A236414 A057873 * A290198 A282153 A054127 Adjacent sequences: A116696 A116697 A116698 * A116700 A116701 A116702 KEYWORD nonn,easy AUTHOR Lara Pudwell, Feb 26 2006 EXTENSIONS Edited by N. J. A. Sloane, Mar 16 2008 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008 STATUS approved

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Last modified December 3 23:05 EST 2022. Contains 358543 sequences. (Running on oeis4.)