A008431 Theta series of D_9 lattice.

1, 144, 2034, 7392, 22608, 44640, 93984, 141120, 262386, 343536, 557280, 703584, 1068384, 1234080, 1851264, 2057280, 2884176, 3231936, 4428242, 4639392, 6455520, 6670272, 8814816, 9320256, 12065568, 12152880, 16161120, 16124544, 20496960, 20906208, 26378880, 25736832

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Programs

Mathematica

terms = 24; s = 1/2 (EllipticTheta[3, 0, q]^9 + EllipticTheta[4, 0, q]^9) + O[q]^(2 terms); CoefficientList[s, q^2] (* Jean-François Alcover, Jul 07 2017 *)

Formula

Expansion of 1/2 (EllipticTheta(3, 0, q)^9 + EllipticTheta(4, 0, q)^9) (formula given by Mathematica's LatticeData(D9)). - Jean-François Alcover, Jul 07 2017

Extensions

More terms from Seiichi Manyama, Oct 16 2018