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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 9 20:55 EDT 2020. Contains 333363 sequences. (Running on oeis4.)