A294726 Number of permutations of [n] avoiding {4231, 3142, 1234}.

1, 1, 2, 6, 21, 71, 217, 599, 1514, 3550, 7801, 16193, 31956, 60282, 109214, 190816, 322679, 529823, 847060, 1321888, 2017991, 3019425, 4435575, 6406973, 9112072, 12775076, 17674931, 24155587, 32637646, 43631516, 57752196, 75735822, 98458109, 126954829, 162444470

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 2 No 28.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

From Colin Barker, Nov 10 2017: (Start)

G.f.: (1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

a(n) = (40320 - 14640*n + 15724*n^2 - 3780*n^3 + 3885*n^4 - 1680*n^5 + 546*n^6 - 60*n^7 + 5*n^8) / 40320.

(End)

Maple

cn := [1, -8, 29, -60, 81, -70, 40, -10, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^9 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Nov 10 2017

Crossrefs

Sequence in context: A116755 A116833 A116808 * A294700 A294701 A116749

Adjacent sequences: A294723 A294724 A294725 * A294727 A294728 A294729

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved