A116766 Number of permutations of length n which avoid the patterns 2134, 3421, 4312.

1, 2, 6, 21, 71, 200, 465, 929, 1667, 2766, 4325, 6455, 9279, 12932, 17561, 23325, 30395, 38954, 49197, 61331, 75575, 92160, 111329, 133337, 158451, 186950, 219125, 255279, 295727, 340796

Offset

1,2

Links

Table of n, a(n) for n=1..30.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 19.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -((6x^8-7x^7-7x^6+4x^5+11x^4+x^3+6x^2-3x+1)*x)/(x-1)^5.

For n >= 5, a(n) = (n^4 - 5n^3 + 9n^2 - 57n + 202)/2. - Franklin T. Adams-Watters, Sep 16 2006

Mathematica

(1 - 3x + 6x^2 + x^3 + 11x^4 + 4x^5 - 7x^6 - 7x^7 + 6x^8)/(1 - x)^5 + O[x]^30 // CoefficientList[#, x]& (* Jean-François Alcover, May 06 2017 *)

Crossrefs

Sequence in context: A116794 A294719 A116795 * A116825 A116767 A116759

Adjacent sequences: A116763 A116764 A116765 * A116767 A116768 A116769

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved