A005877 - OEIS

%I M3322 #20 Dec 01 2017 03:03:37

%S 4,8,8,16,12,8,24,16,16,24,16,16,28,32,8,32,32,16,40,16,16,40,40,32,

%T 36,16,24,48,32,24,40,48,16,56,32,16,64,40,32,32,36,40,48,48,32,48,48,

%U 16,80,40,24,80

%N Theta series of cubic lattice with respect to square.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A005877/b005877.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/cubicP.html">Home page for this lattice</a>

%F a(n) = 4*A045828(n).

%t terms = 52; QP = QPochhammer; s = 4*(QP[q^2]^3*QP[q^4]^2)/QP[q]^2 + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 05 2017 *)

%Y Cf. A045828.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_