A116727 Number of permutations of length n which avoid the patterns 321, 2134, 3412.

1, 2, 5, 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 302, 312, 322, 332, 342, 352, 362, 372, 382, 392, 402, 412, 422, 432, 442, 452, 462, 472, 482, 492, 502, 512, 522

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 (2,-1).

Formula

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

For n >= 4, a(n) = 10*n - 28. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 2*a(n-1) - a(n-2) for n=5. - Colin Barker, Oct 24 2017

Mathematica

Join[{1, 2, 5}, LinearRecurrence[{2, -1}, {12, 22}, 100]] (* Jean-François Alcover, Oct 12 2020 *)

Prog

(PARI) Vec(x*(1 + 2*x^2 + 4*x^3 + 3*x^4) / (1 - x)^2 + O(x^70)) \\ Colin Barker, Oct 24 2017

Crossrefs

Sequence in context: A182201 A106331 A368969 * A116729 A048840 A116718

Adjacent sequences: A116724 A116725 A116726 * A116728 A116729 A116730

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved