A116796 Number of permutations of length n which avoid the patterns 2314, 3241, 4132.

1, 2, 6, 21, 72, 236, 745, 2286, 6866, 20285, 59156, 170712, 488401, 1387226, 3916062, 10996581, 30737760, 85573316, 237387961, 656451270, 1810142186, 4978643597, 13661617196, 37409025456, 102238082977, 278920277426, 759695287350, 2066068144821

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 (7,-17,17,-7,1).

Formula

G.f.: x*(1 - 5*x + 9*x^2 - 4*x^3) / ((1 - x)*(1 - 3*x + x^2)^2).

From Colin Barker, Oct 19 2017: (Start)

a(n) = (1/25)*(2^(-n)*(25*2^n + sqrt(5)*(3-sqrt(5))^n - sqrt(5)*(3+sqrt(5))^n + 10*((3-sqrt(5))^n + (3+sqrt(5))^n)*n)).

a(n) = 7*a(n-1) - 17*a(n-2) + 17*a(n-3) - 7*a(n-4) + a(n-5) for n>5.

(End)

a(n) = 1 + (2*(n - 1)*Lucas(2*(n - 1)) - Fibonacci(2*(n - 1)))/5. - Ehren Metcalfe, Oct 22 2017

Mathematica

 LinearRecurrence[{7, -17, 17, -7, 1}, {1, 2, 6, 21, 72}, 80] (* Vincenzo Librandi, Oct 22 2017 *)

Prog

(PARI) Vec(x*(1 - 5*x + 9*x^2 - 4*x^3) / ((1 - x)*(1 - 3*x + x^2)^2) + O(x^40)) \\ Colin Barker, Oct 19 2017
(Magma) [1+(2*(n-1)*Lucas(2*(n-1))-Fibonacci(2*(n-1)))/5: n in [1..30]]; // Vincenzo Librandi, Oct 22 2017

Crossrefs

Sequence in context: A116758 A116838 A116836 * A116779 A116737 A360153

Adjacent sequences: A116793 A116794 A116795 * A116797 A116798 A116799

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved