A272364 Number of integer solutions to a^2 + b^2 + 3*c^2 + 4*d^2 = n.

1, 4, 4, 2, 14, 24, 8, 12, 44, 36, 8, 24, 50, 40, 24, 16, 50, 96, 28, 12, 112, 96, 24, 48, 104, 68, 56, 50, 60, 168, 40, 12, 188, 144, 32, 48, 182, 104, 72, 76, 88, 240, 48, 60, 240, 168, 48, 96, 230, 124, 84, 64, 196, 312, 80, 48, 312, 264, 56, 120, 160, 200, 120, 60

Offset: 0

Author

Seiichi Manyama, Oct 06 2018

Keywords

• nonn

Comments

a(n) > 0 for n >= 0.

References

• J. H. Conway, Universal quadratic forms and the fifteen theorem, Contemporary Mathematics 272 (1999), 23-26.

Links

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

Crossrefs

Cf. A034896, A320147, A320148.

Formula

G.f.: theta_3(q)^2 * theta_3(q^3) * theta_3(q^4).