A116793 Number of permutations of length n which avoid the patterns 1432, 2143, 3124; or avoid the patterns 1432, 2314, 3142.

1, 2, 6, 21, 74, 253, 845, 2791, 9188, 30246, 99639, 328422, 1082797, 3570197, 11771589, 38812310, 127966990, 421913905, 1391070390, 4586427029, 15121681789, 49856965951, 164381014292, 541972783322, 1786912535551

Offset

1,2

Links

Harvey P. Dale, 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 (6,-12,11,-3,1).

Formula

G.f.: A(x) = -{(x^4-2x^3+6x^2-4x+1)x}/{x^5-3x^4+11x^3-12x^2+6x-1}

Mathematica

LinearRecurrence[{6, -12, 11, -3, 1}, {1, 2, 6, 21, 74}, 30] (* Harvey P. Dale, Feb 27 2021 *)

Crossrefs

Sequence in context: A116780 A116777 A294768 * A294805 A116805 A116790

Adjacent sequences: A116790 A116791 A116792 * A116794 A116795 A116796

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved