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A051531
Molien series for group H_{1,3}^{8} of order 2304.
1
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
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.
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
KEYWORD
nonn,easy,nice
STATUS
approved