A008427 Theta series of {D_8}* lattice.

1, 16, 368, 448, 3184, 2016, 10304, 5504, 25712, 12112, 46368, 21312, 89152, 35168, 126592, 56448, 205936, 78624, 278576, 109760, 401184, 154112, 490176, 194688, 719936, 252016, 808864, 327040

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

G.f.: (theta_3(q))^8 + (theta_2(q))^8.

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (5/4) * Pi^2 / Gamma(3/4)^8 = A388187. - Simon Plouffe, Sep 15 2025

Mathematica

terms = 28; s = EllipticTheta[3, 0, q]^8 + EllipticTheta[2, 0, q]^8 + O[q]^terms; CoefficientList[s, q] (* Jean-François Alcover, Jul 04 2017 *)

Crossrefs

Cf. A008430, A109772.

Sequence in context: A276257 A276097 A265476 * A187177 A053105 A220576

Adjacent sequences: A008424 A008425 A008426 * A008428 A008429 A008430

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved