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

0,2

Links

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

Formula

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

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/800) * Pi * 5^(3/4) * sqrt(2) * (5-5^(1/2))^(3/2) * (5^(1/2)+1)^3 / Gamma(3/4)^4 = A388825. - Simon Plouffe, Sep 18 2025

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 *)

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.

Sequence in context: A281484 A236931 A028659 * A028643 A236923 A028627

Adjacent sequences: A236927 A236928 A236929 * A236931 A236932 A236933

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2014

Status

approved