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A008665
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Theta series of direct sum of 2 copies of b.c.c. lattice.
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1
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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
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OFFSET
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0,4
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116.
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LINKS
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FORMULA
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G.f.: (theta_3(z)*theta_3(z)*theta_3(z)+theta_2(z)*theta_2(z)*theta_2(z))^2.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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