A116713 Number of permutations of length n which avoid the patterns 123, 2431, 4132.

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

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