A236925 Number of integer solutions to a^2 + 4*b^2 + 4*c^2 + 4*d^2 = n.

1, 2, 0, 0, 8, 12, 0, 0, 24, 26, 0, 0, 32, 28, 0, 0, 24, 36, 0, 0, 48, 64, 0, 0, 96, 62, 0, 0, 64, 60, 0, 0, 24, 96, 0, 0, 104, 76, 0, 0, 144, 84, 0, 0, 96, 156, 0, 0, 96, 114, 0, 0, 112, 108, 0, 0, 192, 160, 0, 0, 192, 124, 0, 0, 24, 168, 0, 0, 144, 192, 0

Offset

0,2

Links

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

Olivia X. M. Yao, Ernest X. W. Xia, Combinatorial proofs of five formulas of Liouville, Discrete Math. 318 (2014), 1--9. MR3141622.

Formula

Yao and Xia give an explicit formula for a(n) due to Liouville.

G.f.: theta_3(q)*theta_3(q^4)^3, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 03 2018

Crossrefs

Cf. A000118.

Sequence in context: A215122 A332473 A235789 * A134414 A113036 A000425

Adjacent sequences: A236922 A236923 A236924 * A236926 A236927 A236928

Keyword

nonn,look

Author

N. J. A. Sloane, Feb 14 2014

Status

approved