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A008665 Theta series of direct sum of 2 copies of b.c.c. lattice. 1
1, 0, 0, 16, 12, 0, 64, 96, 60, 0, 0, 240, 160, 0, 384, 416, 252, 0, 0, 720, 312, 0, 960, 1056, 544, 0, 0, 1312, 960, 0, 1664, 1920, 1020, 0, 0, 2496, 876, 0, 2880, 2720, 1560, 0, 0, 3696, 2400, 0, 4224, 4416 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116.
LINKS
FORMULA
G.f.: (theta_3(z)*theta_3(z)*theta_3(z)+theta_2(z)*theta_2(z)*theta_2(z))^2.
MATHEMATICA
terms = 48; t2 = EllipticTheta[2, 0, z]; t3 = EllipticTheta[3, 0, z]; s = Normal[(t3^3 + t2^3)^2 + O[z]^terms] /. z -> z^4 // Simplify[#, z > 0]&; CoefficientList[s, z][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)
CROSSREFS
Sequence in context: A225842 A298450 A028695 * A076823 A070551 A028493
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)