A004670 Theta series of extremal even unimodular lattice in dimension 32.

1, 0, 146880, 64757760, 4844836800, 137695887360, 2121555283200, 21421110804480, 158757684004800, 928986331545600, 4512164186816640, 18847854517248000, 69519016873985280, 230952108679004160

Offset

0,3

Comments

There are at least 15 such lattices, one of which is the Barnes-Wall lattice BW_32.

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 195.

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

N. Elkies, Rational Lattices and their Theta Functions

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; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

G. Nebe and N. J. A. Sloane, Home page for this lattice

Index entries for sequences related to Barnes-Wall lattices

Formula

a(n) = A282012(n) - 960*A027364(n-1) for n > 0. - Andy Huchala, May 01 2021

Example

G.f.: 1 + 146880*q^2 + 64757760*q^3 + 4844836800*q^4 + ...

Prog

(Sage)
e4 = eisenstein_series_qexp(4, 20, normalization = "integral");
delta = CuspForms(1, 12).0.q_expansion(20);
(e4^4 - 960*delta*e4).list()[:20] # Andy Huchala, May 01 2021

Crossrefs

Cf. A027364, A282012.

Sequence in context: A345753 A110084 A224587 * A111044 A189789 A204105

Adjacent sequences: A004667 A004668 A004669 * A004671 A004672 A004673

Keyword

nonn

Author

N. J. A. Sloane

Status

approved