A294695 Number of permutations of [n] avoiding {1243, 2431, 3412}.

1, 1, 2, 6, 21, 73, 240, 748, 2240, 6525, 18653, 52640, 147210, 408957, 1130398, 3112172, 8540753, 23375439, 63830072, 173949534, 473211976, 1285299971, 3486071977, 9442928926, 25548319586, 69046732343, 186416183910, 502821645418, 1355067144205, 3648781579445, 9817397466928

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 1342 and two other 4-letter patterns, arXiv:1708.00832 (2017). Table 1 No 90.

Index entries for linear recurrences with constant coefficients, signature (12,-61,172,-296,322,-221,92,-21,2).

Formula

O.g.f.: (1 - 11*x + 51*x^2 - 129*x^3 + 195*x^4 - 183*x^5 + 104*x^6 - 30*x^7 + 3*x^8) / ((1 - x)^4*(1 - 2*x)*(1 - 3*x + x^2)^2).

a(n) = 12*a(n-1) - 61*a(n-2) + 172*a(n-3) - 296*a(n-4) + 322*a(n-5) - 221*a(n-6) + 92*a(n-7) - 21*a(n-8) + 2*a(n-9) for n>8. - Colin Barker, Nov 07 2017

Maple

p := 1-11*x+51*x^2-129*x^3+195*x^4-183*x^5+104*x^6-30*x^7+3*x^8 ;
q := (1-x)^4*(1-2*x)*(1-3*x+x^2)^2 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 11*x + 51*x^2 - 129*x^3 + 195*x^4 - 183*x^5 + 104*x^6 - 30*x^7 + 3*x^8) / ((1 - x)^4*(1 - 2*x)*(1 - 3*x + x^2)^2) + O(x^30)) \\ Colin Barker, Nov 07 2017

Crossrefs

Sequence in context: A116740 A294802 A116788 * A116778 A116787 A294803

Adjacent sequences: A294692 A294693 A294694 * A294696 A294697 A294698

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved