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 A116735 Number of permutations of length n which avoid the patterns 231, 1234, 4312; or avoid the patterns 312, 1234, 1432, etc. 2
 1, 2, 5, 12, 23, 38, 57, 80, 107, 138, 173, 212, 255, 302, 353, 408, 467, 530, 597, 668, 743, 822, 905, 992, 1083, 1178, 1277, 1380, 1487, 1598, 1713, 1832, 1955, 2082, 2213, 2348, 2487, 2630, 2777, 2928, 3083, 3242, 3405, 3572, 3743, 3918, 4097, 4280, 4467 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of permutations pi of length n such that pi and pi^2 both avoid 132 and 3421. - Colin Defant, Jul 24 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Miklos Bona and Rebecca Smith, Pattern Avoidance in Permutations and Their Squares, arXiv:1901.00026 [math.CO], 2019. Amanda Burcroff and Colin Defant, Pattern-Avoiding Permutation Powers, arXiv:1907.09451 [math.CO], 2019. Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005. Index entries for linear recurrences with constant coefficients, signature (3, -3, 1). FORMULA G.f.: x*(1 - x + 2*x^2 + 2*x^3)/(1-x)^3. For n >= 2, a(n) = 2*n^2 - 7*n + 8. - Franklin T. Adams-Watters, Sep 16 2006 a(n) = A096376(n-2), n > 1. - R. J. Mathar, Aug 10 2008 E.g.f.: -8 - 2*x + (8 - 5*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 10 2019 MAPLE A116735:=n->`if`(n=1, 1, 2*n^2-7*n+8); seq(A116735(n), n=1..50); # G. C. Greubel, Aug 10 2019 MATHEMATICA Join[{1}, LinearRecurrence[{3, -3, 1}, {2, 5, 12}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *) PROG (PARI) vector(50, n, if(n<2, n, 2*n^2-7*n+8)) \\ G. C. Greubel, Aug 10 2019 (Magma) [n lt 2 select n else 2*n^2-7*n+8: n in [1..50]]; // G. C. Greubel, Aug 10 2019 (Sage) [1]+[2*n^2-7*n+8 for n in (2..50)] # G. C. Greubel, Aug 10 2019 (GAP) Concatenation([1], List([2..50], n-> 2*n^2-7*n+8)); # G. C. Greubel, Aug 10 2019 CROSSREFS Sequence in context: A247658 A109653 A115520 * A096376 A357288 A326510 Adjacent sequences: A116732 A116733 A116734 * A116736 A116737 A116738 KEYWORD nonn,easy AUTHOR Lara Pudwell, Feb 26 2006 STATUS approved

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Last modified August 13 15:25 EDT 2024. Contains 375142 sequences. (Running on oeis4.)