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A004670 Theta series of extremal even unimodular lattice in dimension 32. 1
1, 0, 146880, 64757760, 4844836800, 137695887360, 2121555283200, 21421110804480, 158757684004800, 928986331545600, 4512164186816640, 18847854517248000, 69519016873985280, 230952108679004160 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 09:17 EDT 2022. Contains 357270 sequences. (Running on oeis4.)