A294796 Number of permutations of [n] avoiding {1234, 1324, 3412}.

1, 1, 2, 6, 21, 73, 236, 700, 1919, 4927, 12006, 28090, 63705, 141109, 307088, 659576, 1402947, 2962699, 6223018, 13018294, 27148925, 56478465, 117258996, 243044020, 503038535, 1039847767, 2147071790, 4428689074, 9126212193, 18789776461, 38653871640, 79455914224

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 1 No 69.

Index entries for linear recurrences with constant coefficients, signature (10,-43,104,-155,146,-85,28,-4).

Formula

G.f.: (1 - 9*x + 35*x^2 - 75*x^3 + 98*x^4 - 78*x^5 + 34*x^6 - 10*x^7) / ((1 - x)^6*(1 - 2*x)^2).

From Colin Barker, Nov 09 2017: (Start)

a(n) = -5 + 3*2^(1+n) + (-169/30+2^n)*n - (3*n^2)/2 - (5*n^3)/6 - n^5/30.

a(n) = 10*a(n-1) - 43*a(n-2) + 104*a(n-3) - 155*a(n-4) + 146*a(n-5) - 85*a(n-6) + 28*a(n-7) - 4*a(n-8) for n>7.

(End)

Maple

(1-9*x+35*x^2-75*x^3+98*x^4-78*x^5+34*x^6-10*x^7)/((1-2*x)^2*(1-x)^6) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;

Mathematica

LinearRecurrence[{10, -43, 104, -155, 146, -85, 28, -4}, {1, 1, 2, 6, 21, 73, 236, 700}, 40] (* Harvey P. Dale, Nov 23 2022 *)

Prog

(PARI) Vec((1 - 9*x + 35*x^2 - 75*x^3 + 98*x^4 - 78*x^5 + 34*x^6 - 10*x^7) / ((1 - x)^6*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Nov 09 2017

Crossrefs

Sequence in context: A116783 A116739 A116770 * A116753 A294762 A294797

Adjacent sequences: A294793 A294794 A294795 * A294797 A294798 A294799

Keyword

nonn,easy

Author

R. J. Mathar, Nov 09 2017

Status

approved