A294801 Number of permutations of [n] avoiding {4231, 1324, 2341}.

1, 1, 2, 6, 21, 73, 239, 736, 2158, 6102, 16813, 45493, 121567, 322108, 848654, 2227722, 5834253, 15258361, 39874967, 104169568, 272109046, 710846406, 1857283957, 4853664901, 12686932951, 33169384588, 86737334054, 226858067466, 593434214373, 1552572159577, 4062403215263, 10630610953408

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 84.

Index entries for linear recurrences with constant coefficients, signature (10,-41,89,-110,77,-28,4).

Formula

From Colin Barker, Apr 25 2020: (Start)

G.f.: (1 - 9*x + 33*x^2 - 62*x^3 + 64*x^4 - 36*x^5 + 7*x^6) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x + x^2)).

a(n) = 10*a(n-1) - 41*a(n-2) + 89*a(n-3) - 110*a(n-4) + 77*a(n-5) - 28*a(n-6) + 4*a(n-7) for n>6.

(End)

Maple

(1 -9*x +33*x^2 -62*x^3 +64*x^4 -36*x^5 +7*x^6)/((1 -3*x +x^2)*(1 -2*x)^2*(1 -x)^3) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 9*x + 33*x^2 - 62*x^3 + 64*x^4 - 36*x^5 + 7*x^6) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x + x^2)) + O(x^40)) \\ Colin Barker, Apr 25 2020

Crossrefs

Sequence in context: A294800 A116776 A116754 * A116768 A294694 A116740

Adjacent sequences: A294798 A294799 A294800 * A294802 A294803 A294804

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved