A294701 Number of permutations of [n] avoiding {4231, 2143, 1342}.

1, 1, 2, 6, 21, 71, 218, 614, 1619, 4065, 9840, 23168, 53393, 120995, 270518, 598218, 1310943, 2851061, 6160652, 13238564, 28311869, 60293463, 127926642, 270533006, 570425771, 1199571401, 2516582888, 5268046344, 11005854249, 22951232075, 47781511790, 99321119378

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 (2017), Table 1 No 30.

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

Formula

O.g.f.: (1 - 6*x + 14*x^2 - 14*x^3 + 8*x^4 - 2*x^6)/((1 - x)^3*(1 - 2*x)^2).

a(n) = (28 - 32*2^n + 22*n + 7*2^n*n + 2*n^2)/4 for n>1. - Bruno Berselli, Nov 07 2017

a(n) = 7*a(n-1) - 19*a(n-2) + 25*a(n-3) - 16*a(n-4) + 4*a(n-5) for n>4. - Colin Barker, Nov 10 2017

Maple

p := 1-6*x+14*x^2-14*x^3+8*x^4-2*x^6 ;
q := (1-x)^3*(1-2*x)^2 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 6*x + 14*x^2 - 14*x^3 + 8*x^4 - 2*x^6)/((1 - x)^3*(1 - 2*x)^2) + O(x^40)) \\ Colin Barker, Nov 10 2017

Crossrefs

Sequence in context: A116808 A294726 A294700 * A116749 A116792 A116761

Adjacent sequences: A294698 A294699 A294700 * A294702 A294703 A294704

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved