A116711 Number of permutations of length n which avoid the patterns 123, 3214, 4312.

1, 2, 5, 12, 23, 36, 51, 68, 87, 108, 131, 156, 183, 212, 243, 276, 311, 348, 387, 428, 471, 516, 563, 612, 663, 716, 771, 828, 887, 948, 1011, 1076, 1143, 1212, 1283, 1356, 1431, 1508, 1587, 1668, 1751, 1836, 1923, 2012, 2103, 2196, 2291, 2388, 2487, 2588

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 (3,-3,1).

Formula

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

For n >= 4, a(n) = n^2 + 2*n - 12. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. - Colin Barker, Oct 23 2017

Prog

(PARI) Vec(x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Oct 23 2017

Crossrefs

Sequence in context: A123647 A166249 A326762 * A247658 A109653 A115520

Adjacent sequences: A116708 A116709 A116710 * A116712 A116713 A116714

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved