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%I #6 Mar 30 2012 18:54:36
%S 1,0,108,0,710532,24440832,566075628,7732703232,74944737972,
%T 554813521920,3327318944136,16817973387264,73810502037252,
%U 287829235703808,1014561529824096,3277805665185792,9820673253392148,27525159583211520,72722364748416108
%N 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).
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd, 1999.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%F 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).
%Y Cf. A014487, A109006.
%K nonn
%O 0,3
%A _N. J. A. Sloane_ and _Nadia Heninger_, Aug 16 2005
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