A051531 Molien series for group H_{1,3}^{8} of order 2304.

1, 1, 4, 15, 24, 44, 81, 115, 168, 247, 322, 424, 561, 693, 860, 1071, 1276, 1524, 1825, 2119, 2464, 2871, 3270, 3728, 4257, 4777, 5364, 6031, 6688, 7420, 8241, 9051, 9944, 10935, 11914, 12984, 14161, 15325, 16588, 17967, 19332, 20804

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Formula

G.f. ( 1-x+3*x^2+6*x^3+5*x^5+2*x^6 ) / ( (1+x+x^2)^2*(x-1)^4 ). - R. J. Mathar, Oct 01 2011

a(0)=1, a(1)=1, a(2)=4, a(3)=15, a(4)=24, a(5)=44, a(6)=81, a(7)=115, a(n)= 2*a(n-1)- a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8). - Harvey P. Dale, Jan 12 2013

a(n) ~ 8/27*n^3. - Ralf Stephan, May 17 2014

Maple

(1+2*x^2+9*x^3+6*x^4+5*x^5+7*x^6+2*x^7)/((1-x)*(1-x^2)*(1-x^3)^2);

Mathematica

CoefficientList[Series[(1-x+3x^2+6x^3+5x^5+2x^6)/((1+x+x^2)^2(x-1)^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {1, 1, 4, 15, 24, 44, 81, 115}, 50] (* Harvey P. Dale, Jan 12 2013 *)

Crossrefs

Sequence in context: A267769 A192201 A054308 * A062835 A203231 A171788

Adjacent sequences: A051528 A051529 A051530 * A051532 A051533 A051534

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved