A005925 Theta series of diamond.

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, 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, 0, 6, 0, 0, 12

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

a(n) > 0 iff n is in A047470. - Robert Israel, Jul 06 2016

References

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

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 120.
• G. L. Hall, Comment on the paper "Theta series and magic numbers for diamond and certain ionic crystal structures" [J. Math. Phys. 28, 1653 (1987)]. Journal of Mathematical Physics; Sep. 1988, Vol. 29 Issue 9, pp. 2090-2092. - From _N. J. A. Sloane_, Dec 18 2012
• N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657.

Crossrefs

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

Programs

Maple

S:= series((JacobiTheta2(0,z^4)^3 + JacobiTheta3(0,z^4)^3 + JacobiTheta4(0,z^4)^3)/2, z, 101):
seq(coeff(S,z,j),j=0..100); # Robert Israel, Jul 06 2016

Mathematica

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 *)

Formula

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