A294804 Number of permutations of [n] avoiding {1324, 3142, 4231}.

1, 1, 2, 6, 21, 73, 242, 762, 2290, 6610, 18434, 49922, 131842, 340738, 864258, 2156546, 5304322, 12881922, 30932994, 73531394, 173211650, 404684802, 938475522, 2161639426, 4948230146, 11262754818, 25501368322, 57461964802, 128899350530, 287947358210, 640755433474, 1420694650882, 3139352657922, 6915165782018

Offset

0,3

Links

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

D. Callan and T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 1 No 99.

Index entries for linear recurrences with constant coefficients, signature (9,-32,56,-48,16).

Formula

G.f.: (1 - 8*x + 25*x^2 - 36*x^3 + 23*x^4 - 4*x^5 + x^6) / ((1 - x)*(1 - 2*x)^4).

From Colin Barker, Nov 09 2017: (Start)

a(n) = (1/192)*(384 - 51*2^(2+n) + 17*2^(3+n)*n - 27*2^n*n^2 + 5*2^n*n^3) for n>1.

a(n) = 9*a(n-1) - 32*a(n-2) + 56*a(n-3) - 48*a(n-4) + 16*a(n-5) for n>6.

(End)

Maple

(1 -8*x +25*x^2 -36*x^3 +23*x^4 -4*x^5 +x^6)/((1 -x)*(1 -2*x)^4) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{9, -32, 56, -48, 16}, {1, 1, 2, 6, 21, 73, 242}, 40] (* Harvey P. Dale, Jul 22 2020 *)

Prog

(PARI) Vec((1 - 8*x + 25*x^2 - 36*x^3 + 23*x^4 - 4*x^5 + x^6) / ((1 - x)*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A116843 A116822 A116797 * A116744 A165521 A294696

Adjacent sequences: A294801 A294802 A294803 * A294805 A294806 A294807

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved