A294817 Number of permutations of [n] avoiding {1324, 2431, 3241}.

1, 1, 2, 6, 21, 76, 270, 927, 3074, 9886, 30985, 95064, 286558, 851203, 2497550, 7252494, 20874861, 59630404, 169225518, 477513639, 1340705306, 3747697726, 10435070737, 28954040496, 80087091646, 220897122571, 607726482470, 1668084221742, 4568859998709, 12489795988636

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 1 No 184.

Index entries for linear recurrences with constant coefficients, signature (9,-31,51,-41,15,-2).

Formula

From Colin Barker, Nov 23 2017: (Start)

a(n) = (1/25)*(2^(-1-n)*(-25*2^(1+n) + 75*2^(1+2*n) - 25*(3+sqrt(5))^n - 37*sqrt(5)*(3+sqrt(5))^n + (3-sqrt(5))^n*(-25+37*sqrt(5)) + 20*((3-sqrt(5))^n + (3+sqrt(5))^n)*n)).

a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 41*a(n-4) + 15*a(n-5) - 2*a(n-6) for n>5.

(End)

Maple

(1 -8*x +24*x^2 -32*x^3 +19*x^4 -3*x^5)/((1 -x)*(1 -2*x)*(1 -3*x +x^2)^2) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 -8*x +24*x^2 -32*x^3 +19*x^4 -3*x^5)/((1 -x)*(1 -2*x)*(1 -3*x +x^2)^2) + O(x^40)) \\ Colin Barker, Nov 23 2017

Crossrefs

Sequence in context: A148490 A006612 A116769 * A294772 A294818 A116809

Adjacent sequences: A294814 A294815 A294816 * A294818 A294819 A294820

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved