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A051462 Molien series for group G_{1,2}^{8} of order 1536. 1
1, 4, 11, 25, 48, 83, 133, 200, 287, 397, 532, 695, 889, 1116, 1379, 1681, 2024, 2411, 2845, 3328, 3863, 4453, 5100, 5807, 6577, 7412, 8315, 9289, 10336, 11459, 12661, 13944, 15311, 16765, 18308, 19943, 21673, 23500, 25427, 27457, 29592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the Clifford-Weil group for complete weight enumerators of codes over Z/4Z of Type 4_{II}^Z.

LINKS

T. D. Noe, 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.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. [Eq. (8.2.18), p. 233.]

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

FORMULA

Third differences are periodic with period 3.

a(n) = 1 + n + 2n^2 + 3[(n + 2)((n-1)^2)/18] + 2[(n + 1)((n-2)^2)/18] + 3[n((n-3)^2)/18] (where [..] denotes the floor function). - John W. Layman, Nov 22 2000

a(0)=1, a(1)=4, a(2)=11, a(3)=25, a(4)=48, a(5)=83, a(n)=3*a(n-1)- 3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6). - Harvey P. Dale_, Jun 06 2011

G.f.: ((x+1)(x^2+1)^2)/((x-1)^4(x^2+x+1)). - Harvey P. Dale, Jun 06 2011

MAPLE

(1+x)*(1+x^2)^2/((1-x)^3*(1-x^3));

MATHEMATICA

LinearRecurrence[{3, -3, 2, -3, 3, -1}, {1, 4, 11, 25, 48, 83}, 40] (* or *) CoefficientList[Series[(1+x)(1+x^2)^2/((1-x)^3(1-x^3)), {x, 0, 40}], x] (* Harvey P. Dale, Jun 06 2011 *)

CROSSREFS

Sequence in context: A176959 A115294 A110610 * A006004 A290876 A006522

Adjacent sequences:  A051459 A051460 A051461 * A051463 A051464 A051465

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)