A169784 Number of solutions to a^2 + b^2 + 5*c^2 = n.

1, 4, 4, 0, 4, 10, 8, 8, 4, 12, 24, 0, 0, 16, 8, 16, 4, 8, 20, 0, 10, 16, 24, 8, 8, 44, 8, 0, 8, 16, 40, 16, 4, 16, 24, 0, 12, 32, 8, 16, 24, 16, 16, 0, 0, 50, 40, 8, 0, 28, 44, 0, 16, 16, 32, 40, 8, 32, 40, 0, 16, 32, 16, 24, 4, 48, 16, 0, 8, 16, 80, 16, 20, 40, 24, 0, 0, 16, 32, 32, 10, 36

Offset

0,2

Comments

a(n) = 0 for n of the form 4^i*(8*j+3), A055046. [Zak Seidov, May 12 2010]

Links

Zak Seidov, Table of n,a(n) for n=0..1000

Formula

G.f.: theta_3(q)^2*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) = (8/125) * Pi^(3/4) * 2^(3/5) * 5^(1/4) * Gamma(9/10)^3 * Gamma(7/10)^3 * (5+5^(1/2))^3 * (1/4*5^(1/2)-1/4)^3 * (1/4*5^(1/2)+1/4)^3 / Gamma(3/4)^3 / Gamma(4/5)^6 = A388685. - Simon Plouffe, Sep 18 2025

Crossrefs

x^2+y^2+k*z^2: A005875, A014455, A034933, A169783.

Sequence in context: A253185 A028658 A241535 * A236929 A351521 A028642

Adjacent sequences: A169781 A169782 A169783 * A169785 A169786 A169787

Keyword

nonn

Author

N. J. A. Sloane, May 12 2010

Status

approved