A116721 Number of permutations of length n which avoid the patterns 123, 3142, 4312; or avoid the patterns 123, 3421, 4231.

1, 2, 5, 12, 24, 42, 67, 100, 142, 194, 257, 332, 420, 522, 639, 772, 922, 1090, 1277, 1484, 1712, 1962, 2235, 2532, 2854, 3202, 3577, 3980, 4412, 4874, 5367, 5892, 6450, 7042, 7669, 8332, 9032, 9770, 10547, 11364, 12222, 13122, 14065, 15052, 16084, 17162

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 (4,-6,4,-1).

Formula

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

For n >= 2, a(n) = (n^3 + 3n^2 - 16n + 24)/6. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5. - Colin Barker, Oct 24 2017

Maple

A116721 := proc(n) coeftayl(-x*(x^4-3*x^2+2*x-1)/(x-1)^4, x=0, n) ; end: seq(A116721(n), n=1..60) ; # R. J. Mathar, Jan 23 2008

Prog

(PARI) Vec(x*(1 - 2*x + 3*x^2 - x^4) / (1 - x)^4 + O(x^100)) \\ Colin Barker, Oct 24 2017

Crossrefs

Sequence in context: A112287 A127787 A116733 * A294868 A192981 A116713

Adjacent sequences: A116718 A116719 A116720 * A116722 A116723 A116724

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from R. J. Mathar, Jan 23 2008

Status

approved