A320200 Number of integer solutions to a^2 + 2*b^2 + 4*c^2 + 12*d^2 = n.

1, 2, 2, 4, 4, 4, 8, 8, 6, 6, 8, 4, 10, 16, 4, 16, 20, 16, 26, 28, 20, 20, 40, 16, 24, 38, 8, 32, 40, 20, 20, 40, 22, 32, 64, 24, 28, 48, 40, 40, 56, 16, 16, 52, 20, 52, 32, 32, 50, 62, 62, 32, 80, 36, 80, 80, 28, 68, 40, 52, 80, 80, 20, 56, 84, 48, 100, 100, 32, 64

Offset

0,2

Comments

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

Links

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

Formula

G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^4) * theta_3(q^12).

Crossrefs

Cf. A320193, A320194, A320195, A320196, A033720, A320197, A320198, A320199, A320201, A320202.

Sequence in context: A033717 A320202 A320201 * A320199 A033756 A320198

Adjacent sequences: A320197 A320198 A320199 * A320201 A320202 A320203

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2018

Status

approved