A005925 Theta series of diamond. (Formerly M3184)

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

0,4

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.

Formula

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

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 *)

Crossrefs

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

Sequence in context: A108708 A290322 A274948 * A333037 A070206 A228368

Adjacent sequences: A005922 A005923 A005924 * A005926 A005927 A005928

Keyword

nonn,nice

Author

N. J. A. Sloane

Status

approved