A004533 Theta series of 12-dimensional unimodular lattice {D_12}^{+}.

1, 0, 264, 2048, 7944, 24576, 64416, 135168, 253704, 475136, 825264, 1284096, 1938336, 2973696, 4437312, 6107136, 8118024, 11354112, 15653352, 19802112, 24832944, 32800768, 42517728, 51523584

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

Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A106212.

Sequence in context: A195672 A123654 A014745 * A231301 A211718 A331769

Adjacent sequences: A004530 A004531 A004532 * A004534 A004535 A004536

Keyword

nonn

Author

N. J. A. Sloane

Status

approved