A294772 Number of permutations of [n] avoiding {4132, 4123, 1243}.

1, 1, 2, 6, 21, 76, 270, 930, 3114, 10196, 32820, 104283, 328048, 1023854, 3175395, 9797833, 30104416, 92174093, 281393563, 856933273, 2604185761, 7899961881, 23928712717, 72385213846, 218724040451, 660278241111, 1991584682200, 6002897801720, 18082374709679

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 186.

Index entries for linear recurrences with constant coefficients, signature (10,-40,83,-97,64,-22,3).

Formula

G.f.: (1 - 9*x + 32*x^2 - 57*x^3 + 55*x^4 - 27*x^5 + 4*x^6) / ((1 - x)^4*(1 - 3*x)*(1 - 3*x + x^2)).

From Colin Barker, Nov 09 2017: (Start)

a(n) = (35/16 + (13*3^n)/16 - ((3-sqrt(5))/2)^n - ((3+sqrt(5))/2)^n - (7*n)/6 + (5*n^2)/8 - n^3/12).

a(n) = 10*a(n-1) - 40*a(n-2) + 83*a(n-3) - 97*a(n-4) + 64*a(n-5) - 22*a(n-6) + 3*a(n-7) for n>6.

(End)

Maple

-(-27*x^5+55*x^4-57*x^3+32*x^2-9*x+1+4*x^6)/((3*x-1)*(x^2-3*x+1)*(x-1)^4) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 9*x + 32*x^2 - 57*x^3 + 55*x^4 - 27*x^5 + 4*x^6) / ((1 - x)^4*(1 - 3*x)*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A006612 A116769 A294817 * A294818 A116809 A116819

Adjacent sequences: A294769 A294770 A294771 * A294773 A294774 A294775

Keyword

nonn,easy

Author

R. J. Mathar, Nov 08 2017

Status

approved