A294694 Number of permutations of [n] avoiding {3412, 4132, 1324}.

1, 1, 2, 6, 21, 73, 239, 740, 2194, 6298, 17653, 48621, 132199, 356040, 952154, 2533014, 6712221, 17734489, 46753127, 123048884, 323441770, 849373210, 2228871757, 5845630221, 15324795631, 40162310568, 105229244354, 275659639590, 722018109189, 1890931558153, 4951850306303

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 [math.CO] (2017). Table 1 No 86.

Index entries for linear recurrences with constant coefficients, signature (8,-25,39,-32,13,-2).

Formula

O.g.f.: (1 - 7*x + 19*x^2 - 24*x^3 + 16*x^4 - 4*x^5 - x^6 + 2*x^7)/((1 - 2*x)*(1 - 3*x + x^2)*(1 - x)^3).

a(n) = 8*a(n-1) - 25*a(n-2) + 39*a(n-3) - 32*a(n-4) + 13*a(n-5) - 2*a(n-6) for n>7. - Colin Barker, Nov 07 2017

Maple

p := 1-7*x+19*x^2-24*x^3+16*x^4-4*x^5-x^6+2*x^7 ;
q := (1-x)^3*(1-2*x)*(1-3*x+x^2) ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 7*x + 19*x^2 - 24*x^3 + 16*x^4 - 4*x^5 - x^6 + 2*x^7) / ((1 - x)^3*(1 - 2*x)*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Nov 07 2017

Crossrefs

Sequence in context: A116754 A294801 A116768 * A116740 A294802 A116788

Adjacent sequences: A294691 A294692 A294693 * A294695 A294696 A294697

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved