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A008665 Theta series of direct sum of 2 copies of b.c.c. lattice. 1

%I #12 Jul 06 2017 08:56:16

%S 1,0,0,16,12,0,64,96,60,0,0,240,160,0,384,416,252,0,0,720,312,0,960,

%T 1056,544,0,0,1312,960,0,1664,1920,1020,0,0,2496,876,0,2880,2720,1560,

%U 0,0,3696,2400,0,4224,4416

%N Theta series of direct sum of 2 copies of b.c.c. lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116.

%H <a href="/index/Ba#bcc">Index entries for sequences related to b.c.c. lattice</a>

%F G.f.: (theta_3(z)*theta_3(z)*theta_3(z)+theta_2(z)*theta_2(z)*theta_2(z))^2.

%t 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-Fran├žois Alcover_, Jul 06 2017 *)

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_.

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Last modified November 29 00:31 EST 2023. Contains 367422 sequences. (Running on oeis4.)