OFFSET
0,3
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)
J. H. Conway, A. M. Odlyzko and N. J. A. Sloane, Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24, Mathematika, 25 (1978), 36-43.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
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.
G. Nebe and N. J. A. Sloane, Home page for this lattice
FORMULA
Expansion of (theta2(q)^12 + theta3(q)^12 + theta4(q)^12)/2 in powers of q.
EXAMPLE
G.f. = 1 + 264*q^2 + 2048*q^3 + 7944*q^4 + 24576*q^5 + 64416*q^6 + ...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved