A294803 Number of permutations of [n] avoiding {1324, 2413, 3421}.

1, 1, 2, 6, 21, 73, 241, 754, 2252, 6471, 18003, 48736, 128878, 333949, 850061, 2130078, 5263536, 12845251, 30998743, 74055916, 175309058, 411566361, 958923057, 2218787146, 5101322596, 11660165503, 26508001691, 59961770424, 135006257622, 302660977141, 675786261013, 1503238554166, 3332089315928

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 93.

Index entries for linear recurrences with constant coefficients, signature (11,-51,129,-192,168,-80,16).

Formula

G.f.: (1 - 10*x + 42*x^2 - 94*x^3 + 120*x^4 - 86*x^5 + 31*x^6 - 3*x^7) / ((1 - x)^3*(1 - 2*x)^4).

From Colin Barker, Nov 09 2017: (Start)

a(n) = (1/32)*(256 - 115*2^(1+n) + (80+79*2^n)*n - 2*(5*2^n-8)*n^2 + 2^n*n^3) for n>0.

a(n) = 11*a(n-1) - 51*a(n-2) + 129*a(n-3) - 192*a(n-4) + 168*a(n-5) - 80*a(n-6) + 16*a(n-7) for n>7.

(End)

Maple

(1 -10*x +42*x^2 -94*x^3 +120*x^4 -86*x^5 +31*x^6 -3*x^7)/((1 -x)^3*(1 -2*x)^4) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 10*x + 42*x^2 - 94*x^3 + 120*x^4 - 86*x^5 + 31*x^6 - 3*x^7) / ((1 - x)^3*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A294695 A116778 A116787 * A116773 A116741 A116843

Adjacent sequences: A294800 A294801 A294802 * A294804 A294805 A294806

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved