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A008427 Theta series of {D_8}* lattice. 5
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 7 20:04 EST 2021. Contains 349585 sequences. (Running on oeis4.)