A320131 Number of integer solutions to a^2 + b^2 + 2*c^2 + 9*d^2 = n.

1, 4, 6, 8, 12, 8, 8, 16, 6, 14, 32, 20, 40, 48, 16, 32, 44, 28, 54, 72, 40, 64, 72, 16, 40, 52, 56, 92, 96, 56, 32, 80, 38, 48, 104, 64, 102, 144, 52, 32, 112, 44, 128, 168, 68, 136, 128, 96, 104, 132, 62, 144, 176, 104, 172, 96, 112, 112, 192, 116, 96, 240, 96, 176

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)^2 * theta_3(q^2) * theta_3(q^9).

Crossrefs

Cf. A097057, A320124, A320125, A320126, A320127, A320128, A320130, A320132, A320133, A320134, A320135, A320136.

Sequence in context: A320134 A320133 A320132 * A320130 A320128 A320127

Adjacent sequences: A320128 A320129 A320130 * A320132 A320133 A320134

Keyword

nonn

Author

Seiichi Manyama, Oct 06 2018

Status

approved