A236931 Number of integer solutions to a^2 + b^2 + c^2 + 6*d^2 = n.

1, 6, 12, 8, 6, 24, 26, 12, 36, 46, 36, 72, 56, 24, 72, 60, 54, 96, 52, 72, 120, 48, 36, 96, 98, 90, 144, 144, 60, 120, 144, 60, 180, 172, 96, 240, 142, 72, 192, 96, 132, 288, 180, 120, 216, 168, 144, 192, 152, 162, 276, 256, 120, 216, 210, 120, 264, 256, 180, 360, 300

Offset: 0

Author

N. J. A. Sloane, Feb 16 2014

Keywords

• nonn

Links

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

Crossrefs

For number of solutions to a^2 + b^2 + c^2 + k*d^2 = n for k = 1, 2, 3, 4, 5, 6, 7, 8, 12 see A000118, A236928, A236926, A236923, A236930, A236931, A236932, A236927, A236933.

Programs

Maple

See A236924.

Formula

G.f.: theta_3(q)^3*theta_3(q^6), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018