A109005 - OEIS

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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

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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