A236930 Number of integer solutions to a^2 + b^2 + c^2 + 5*d^2 = n.

1, 6, 12, 8, 6, 26, 36, 24, 28, 42, 72, 72, 8, 48, 108, 48, 54, 64, 84, 120, 26, 72, 144, 88, 84, 126, 216, 80, 24, 180, 156, 192, 92, 96, 288, 144, 42, 144, 240, 144, 168, 252, 144, 168, 72, 182, 396, 184, 72, 258, 372, 192, 48, 208, 360, 312, 252, 160, 360, 360, 48

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.

Mathematica

Join[{1},Table[Length[Reduce[a^2+b^2+c^2+5d^2==n,{a,b,c,d},Integers]],{n,60}]] (* Harvey P. Dale, Jul 02 2017 *)

Formula

G.f.: theta_3(q)^3*theta_3(q^5), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018