A294806 Number of permutations of [n] avoiding {1324, 3421, 3241}.

1, 1, 2, 6, 21, 75, 259, 852, 2669, 7997, 23043, 64190, 173677, 458255, 1183139, 2997544, 7470237, 18349057, 44497747, 106691218, 253229501, 595589331, 1389361107, 3217028796, 7398749581, 16911430725, 38436598499, 86905975142, 195555225549, 438086659607, 977373490243, 2172179704400, 4810363365437

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 150.

Index entries for linear recurrences with constant coefficients, signature (12,-62,180,-321,360,-248,96,-16).

Formula

G.f.: (1 - 11*x + 52*x^2 - 136*x^3 + 214*x^4 - 204*x^5 + 111*x^6 - 28*x^7) / ((1 - x)^4*(1 - 2*x)^4).

From Colin Barker, Nov 10 2017: (Start)

a(n) = (1/24)*(24*(2^(2 + n)-3) + 5*(2^n-16)*n - 6*(2^n+2)*n^2 + (2^n-4)*n^3).

a(n) = 12*a(n-1) - 62*a(n-2) + 180*a(n-3) - 321*a(n-4) + 360*a(n-5) - 248*a(n-6) + 96*a(n-7) - 16*a(n-8) for n>7.

(End)

Maple

(1 -11*x +52*x^2 -136*x^3 +214*x^4 -204*x^5 +111*x^6 -28*x^7)/((1 -x)^3*(1 -2*x)^3*(1 -3*x +2*x^2)) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 11*x + 52*x^2 - 136*x^3 + 214*x^4 - 204*x^5 + 111*x^6 - 28*x^7) / ((1 - x)^4*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 10 2017

Crossrefs

Sequence in context: A116840 A116841 A116814 * A294807 A294771 A294814

Adjacent sequences: A294803 A294804 A294805 * A294807 A294808 A294809

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved