A008429 Theta series of D_7 lattice.

1, 84, 574, 1288, 3444, 4424, 9240, 11088, 18494, 19740, 34440, 31304, 52808, 52248, 74048, 71120, 110964, 94864, 145222, 132888, 181384, 163856, 249480, 201040, 295960, 264684, 346696, 314272, 454608, 352520, 518336, 452256, 591934, 517216

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			1 + 84*q^2 + 574*q^4 + 1288*q^6 + 3444*q^8 + ...
		

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

Crossrefs

A008451(2n) = a(n).

Programs

Mathematica

terms = 34; s = 1/2 (EllipticTheta[3, 0, q]^7 + EllipticTheta[4, 0, q]^7) + O[q]^(2 terms); CoefficientList[s, q^2] (* Jean-François Alcover, Jul 07 2017 *)

PARI

{a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^7, n))} /* Michael Somos, Nov 03 2006 */

Formula

G.f.: (theta_3(q^(1/2))^7 + theta_4(q^(1/2))^7)/2.