A116851 - OEIS

A116851

Number of permutations of length n which avoid the patterns 321, 31245.

1, 2, 5, 14, 41, 116, 307, 760, 1779, 3986, 8641, 18282, 38005, 78024, 158791, 321236, 647247, 1300630, 2609029, 5227766, 10467521, 20949692, 41917115, 83855504, 167736331, 335502586, 671040297, 1342121570, 2684290669, 5368636176, 10737335311, 21474742572

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-20,30,-25,11,-2).

FORMULA

G.f.: x*(1 - 5*x + 11*x^2 - 11*x^3 + 8*x^4 - 2*x^5) / ((1 - x)^5*(1 - 2*x)).

a(n) = 5*2^n-(n+2)*(n^3+11*n+24)/12. - R. J. Mathar, Jan 12 2013

PROG

(PARI) Vec(x*(1 - 5*x + 11*x^2 - 11*x^3 + 8*x^4 - 2*x^5) / ((1 - x)^5*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 01 2017

CROSSREFS

Sequence in context: A116846 A080558 A116844 * A038989 A116850 A116847

Adjacent sequences: A116848 A116849 A116850 * A116852 A116853 A116854

KEYWORD

nonn,easy

AUTHOR

Lara Pudwell, Feb 26 2006

STATUS

approved

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