A033720 Product theta3(q^d); d | 8.

1, 2, 2, 4, 4, 4, 8, 8, 8, 10, 12, 12, 16, 20, 16, 24, 24, 20, 26, 20, 24, 32, 24, 24, 32, 30, 28, 40, 32, 20, 48, 32, 24, 48, 36, 48, 52, 36, 40, 56, 48, 52, 64, 44, 48, 84, 48, 48, 96, 50, 62, 72, 56, 68, 80, 72, 64

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also number of integer solutions to a^2 +2*b^2 + 4*c^2 + 8*d^2 = n.

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• J. Liouville, Sur la forme x^2 + 2y^2 + 4z^2 + 8t^2, Journal de mathématiques pures et appliquées 2e série, tome 6 (1861), p. 409-416.

Formula

Liouville gives an explicit formula for a(n).