A294762 Number of permutations of [n] avoiding {4231, 1243, 1234}.

1, 1, 2, 6, 21, 73, 237, 702, 1881, 4577, 10216, 21158, 41097, 75561, 132523, 223134, 362589, 571137, 875246, 1308934, 1915277, 2748105, 3873897, 5373886, 7346385, 9909345, 13203156, 17393702, 22675681, 29276201, 37458663, 47526942, 59829877, 74766081, 92789082

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 71.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: (1 - 7*x + 22*x^2 - 38*x^3 + 43*x^4 - 25*x^5 + 17*x^6 + 2*x^7 - 4*x^8) / (1 - x)^8.

From Colin Barker, Nov 11 2017: (Start)

a(n) = (25200 - 52056*n + 48650*n^2 - 20881*n^3 + 4340*n^4 - 154*n^5 - 70*n^6 + 11*n^7) / 5040 for n>0.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Maple

-(4*x^8-2*x^7-17*x^6+25*x^5-43*x^4+38*x^3-22*x^2+7*x-1)/((x-1)^8)   ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 7*x + 22*x^2 - 38*x^3 + 43*x^4 - 25*x^5 + 17*x^6 + 2*x^7 - 4*x^8) / (1 - x)^8 + O(x^40)) \\ Colin Barker, Nov 11 2017

Crossrefs

Sequence in context: A116770 A294796 A116753 * A294797 A294763 A294798

Adjacent sequences: A294759 A294760 A294761 * A294763 A294764 A294765

Keyword

nonn,easy

Author

R. J. Mathar, Nov 08 2017

Status

approved