%I M3227 #33 Jul 07 2017 03:45:09

%S 4,4,8,12,4,12,12,12,16,16,8,8,28,12,20,24,8,16,28,12,16,28,20,32,20,

%T 16,16,32,20,24,28,8,36,44,12,32,36,16,24,20,28,20,56,28,16,40,20,40,

%U 44,12,36,40,20,32,40,16,24,60,32,36,40,24,32,60,24,40,24,20,60,36,24,32,56,32

%N Theta series of b.c.c. lattice with respect to deep hole.

%D Ono and Skinner, Ann. Math., 147 (1998), 453-470.

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

%D N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.

%H T. D. Noe, <a href="/A004024/b004024.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/Ds3.html">Home page for this lattice</a>

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

%F 4*eta(32z)^4/eta(8z) = 4*Sum q^(x^2+2y^2+2z^2), x, y, z >= 1 and odd.

%t max = 73; 4*CoefficientList[ Series[ Product[ (1-q^(4k))^4 / (1-q^k), {k, 1, max}], {q, 0, max}], q] (* _Jean-François Alcover_, Feb 10 2012, after A045831 *)

%t terms = 74; QP = QPochhammer; s = 4 QP[z^4]^4/QP[z] + O[z]^terms; CoefficientList[s, z] (* _Jean-François Alcover_, Jul 07 2017 *)

%Y Equals 4*A045831.

%K nonn,easy,nice

%O 0,1

%A _N. J. A. Sloane_