A116715 - OEIS

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A116715

Number of permutations of length n which avoid the patterns 312, 2341, 4321.

1, 2, 5, 12, 25, 54, 120, 265, 580, 1272, 2796, 6143, 13488, 29619, 65053, 142873, 313771, 689095, 1513390, 3323699, 7299465, 16031000, 35207128, 77321545, 169812767, 372941033, 819049274, 1798787604, 3950478790, 8676000808, 19054143661, 41846514135

(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 (1,1,2,3,1).

FORMULA

G.f.: x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5).

a(n) = a(n-1) + a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5) for n>5. - Colin Barker, Oct 20 2017

PROG

(PARI) Vec(x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5) + O(x^40)) \\ Colin Barker, Oct 20 2017