A116800 Number of permutations of length n which avoid the patterns 1432, 2314, 3241.

1, 2, 6, 21, 72, 232, 712, 2116, 6155, 17629, 49893, 139851, 388899, 1074280, 2950885, 8066698, 21960083, 59566264, 161060160, 434269077, 1168017399, 3134554480, 8395344424, 22445226508, 59911148129, 159681826564, 425035944306, 1129976852988, 3000770763534

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 51.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-14,3).

Formula

G.f.: x*(1 - 5*x + 10*x^2 - 7*x^3 + 3*x^4 - x^5) / ((1 - 3*x + x^2)*(1 - 4*x + 5*x^2 - 3*x^3)).

a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 8*a(n-4) - 11*a(n-5) + 3*a(n-6) for n>6. - Colin Barker, Oct 23 2017

9*a(n) = 9*(A001906(n)+2*A001906(n+1)) -23*A027439(n) +35*A027439(n-1) -40*A027439(n-2), n>1. - R. J. Mathar, Jan 11 2024

Mathematica

LinearRecurrence[{7, -18, 22, -14, 3}, {1, 2, 6, 21, 72, 232}, 30] (* Harvey P. Dale, Dec 20 2018 *)

Prog

(PARI) Vec(x*(1 - 5*x + 10*x^2 - 7*x^3 + 3*x^4 - x^5) / ((1 - 3*x + x^2)*(1 - 4*x + 5*x^2 - 3*x^3)) + O(x^30)) \\ Colin Barker, Oct 23 2017

Crossrefs

Sequence in context: A116747 A116810 A294703 * A116758 A116838 A116836

Adjacent sequences: A116797 A116798 A116799 * A116801 A116802 A116803

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved