A051462 Molien series for group G_{1,2}^{8} of order 1536.

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, 31835, 34189, 36656, 39239

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

Index entries for Molien series

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

a(n) = (1 + 2*(2*n + 1)*(n^2 + n + 4) - (n mod 3))/9. - Stefano Spezia, May 02 2022

Maple

g := (1+x)*(1+x^2)^2/((1-x)^3*(1-x^3)): gser := series(g, x = 0, 95): seq(coeff(gser, x, n), n = 0 .. 40);

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

Cf. A051461, A051463.

Sequence in context: A176959 A115294 A110610 * A006004 A290876 A333643

Adjacent sequences: A051459 A051460 A051461 * A051463 A051464 A051465

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved