cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A004024 Theta series of b.c.c. lattice with respect to deep hole.

This page as a plain text file.
%I A004024 M3227 #33 Jul 07 2017 03:45:09
%S A004024 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 A004024 16,16,32,20,24,28,8,36,44,12,32,36,16,24,20,28,20,56,28,16,40,20,40,
%U A004024 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 A004024 Theta series of b.c.c. lattice with respect to deep hole.
%D A004024 Ono and Skinner, Ann. Math., 147 (1998), 453-470.
%D A004024 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A004024 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 A004024 T. D. Noe, <a href="/A004024/b004024.txt">Table of n, a(n) for n = 0..1000</a>
%H A004024 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 A004024 <a href="/index/Ba#bcc">Index entries for sequences related to b.c.c. lattice</a>
%F A004024 4*eta(32z)^4/eta(8z) = 4*Sum q^(x^2+2y^2+2z^2), x, y, z >= 1 and odd.
%t A004024 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 A004024 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 A004024 Equals 4*A045831.
%K A004024 nonn,easy,nice
%O A004024 0,1
%A A004024 _N. J. A. Sloane_