A236927 Number of integer solutions to a^2 + b^2 + c^2 + 8*d^2 = n.

1, 6, 12, 8, 6, 24, 24, 0, 14, 42, 48, 40, 20, 72, 96, 0, 30, 108, 84, 72, 40, 96, 120, 0, 36, 126, 144, 80, 48, 168, 96, 0, 62, 120, 216, 128, 42, 216, 216, 0, 72, 252, 192, 168, 100, 168, 288, 0, 68, 342, 252, 144, 120, 312, 240, 0, 112, 216, 336, 232, 48, 360, 384

Offset

0,2

Links

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

Liouville, J., Sur la forme X^2 + Y^2 + Z^2 + 8T^2. Journal de mathématiques pures et appliquées 2e série, tome 6 (1861), p. 324-328.

Formula

G.f.: theta_3(q)^3*theta_3(q^8), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018

Maple

See A236924.

Crossrefs

Cf. A236924.

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.

Sequence in context: A213384 A005875 A236933 * A236932 A281484 A236931

Adjacent sequences: A236924 A236925 A236926 * A236928 A236929 A236930

Keyword

nonn

Author

N. J. A. Sloane, Feb 15 2014

Status

approved