A109005 Theta series of 36-dimensional lattice obtained by applying Construction A_c (as in Theorem 26, p. 198, of Conway-Sloane) to the [18,9,8]_4 self-dual code S_18 over GF(4).

1, 0, 108, 0, 710532, 24440832, 566075628, 7732703232, 74944737972, 554813521920, 3327318944136, 16817973387264, 73810502037252, 287829235703808, 1014561529824096, 3277805665185792, 9820673253392148, 27525159583211520, 72722364748416108

Offset

0,3

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd, 1999.

Links

Table of n, a(n) for n=0..18.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Formula

Let W(x, y) = x^18+2754*x^10*y^8+18360*x^8*y^10+77112*x^6*y^12+110160*x^4*y^14+50949*x^2*y^16+2808*y^18 be the weight enumerator of the code; then replace x by phi_0, y by phi_1 (cf. p. 103 and 198 of Conway-Sloane).

Crossrefs

Cf. A014487, A109006.

Sequence in context: A057388 A192071 A025601 * A036196 A304565 A327338

Adjacent sequences: A109002 A109003 A109004 * A109006 A109007 A109008

Keyword

nonn

Author

N. J. A. Sloane and Nadia Heninger, Aug 16 2005

Status

approved