A005925 - OEIS

%I M3184 #28 Dec 18 2021 20:41:29

%S 1,0,0,4,0,0,0,0,12,0,0,12,0,0,0,0,6,0,0,12,0,0,0,0,24,0,0,16,0,0,0,0,

%T 12,0,0,24,0,0,0,0,24,0,0,12,0,0,0,0,8,0,0,24,0,0,0,0,48,0,0,36,0,0,0,

%U 0,6,0,0,12

%N Theta series of diamond.

%C a(n) > 0 iff n is in A047470. - _Robert Israel_, Jul 06 2016

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

%H Robert Israel, <a href="/A005925/b005925.txt">Table of n, a(n) for n = 0..10000</a>

%H J. H. Conway and N. J. A. Sloane, <a href="http://dx.doi.org/10.1007/978-1-4757-2016-7">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, p. 120.

%H G. L. Hall, <a href="http://dx.doi.org/10.1063/1.527833">Comment on the paper "Theta series and magic numbers for diamond and certain ionic crystal structures" [J. Math. Phys. 28, 1653 (1987)]</a>. Journal of Mathematical Physics; Sep. 1988, Vol. 29 Issue 9, pp. 2090-2092. - From _N. J. A. Sloane_, Dec 18 2012

%H N. J. A. Sloane, <a href="http://dx.doi.org/10.1063/1.527472">Theta series and magic numbers for diamond and certain ionic crystal structures</a>, J. Math. Phys. 28 (1987), 1653-1657.

%F (theta_2^3 + theta_3^3 + theta_4^3) / 2.

%p S:= series((JacobiTheta2(0,z^4)^3 + JacobiTheta3(0,z^4)^3 + JacobiTheta4(0,z^4)^3)/2, z, 101):

%p seq(coeff(S,z,j),j=0..100); # _Robert Israel_, Jul 06 2016

%t terms = 68; s = Simplify[Normal[(EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3 + EllipticTheta[4, 0, z^4]^3)/2 + O[z]^terms], z > 0]; CoefficientList[s, z] (* _Jean-François Alcover_, Jul 07 2017 *)

%Y Cf. A005926, A005927, A047470, A217512, A217513, A217514.

%K nonn,nice

%O 0,4

%A _N. J. A. Sloane_