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%I #37 Aug 01 2024 23:14:49
%S 1,0,264,2048,7944,24576,64416,135168,253704,475136,825264,1284096,
%T 1938336,2973696,4437312,6107136,8118024,11354112,15653352,19802112,
%U 24832944,32800768,42517728,51523584
%N Theta series of 12-dimensional unimodular lattice {D_12}^{+}.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
%H Seiichi Manyama, <a href="/A004533/b004533.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)
%H J. H. Conway, A. M. Odlyzko and N. J. A. Sloane, <a href="http://dx.doi.org/10.1112/S0025579300009244">Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24</a>, Mathematika, 25 (1978), 36-43.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D12p.html">Home page for this lattice</a>
%F Expansion of (theta2(q)^12 + theta3(q)^12 + theta4(q)^12)/2 in powers of q.
%e G.f. = 1 + 264*q^2 + 2048*q^3 + 7944*q^4 + 24576*q^5 + 64416*q^6 + ...
%t terms = 24; s = (EllipticTheta[2, 0, q]^12 + EllipticTheta[3, 0, q]^12 + EllipticTheta[4, 0, q]^12)/2 + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 05 2017 *)
%Y Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A106212.
%K nonn
%O 0,3
%A _N. J. A. Sloane_