A236929 Number of integer solutions to a^2 + b^2 + 5*c^2 + 5*d^2 = n.

1, 4, 4, 0, 4, 12, 16, 16, 4, 20, 44, 16, 16, 24, 32, 64, 4, 8, 52, 16, 44, 32, 48, 48, 16, 84, 56, 64, 32, 56, 176, 32, 4, 64, 72, 112, 52, 56, 80, 64, 44, 72, 128, 32, 48, 188, 96, 48, 16, 68, 244, 128, 56, 56, 160, 176, 32, 128, 120, 112, 176, 88, 128, 144, 4, 200

Offset

0,2

Links

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

J. Liouville, Sur la forme x^2 + 2y^2 + 4z^2 + 8t^2, Journal de mathématiques pures et appliquées 2e série, tome 6 (1861), p. 409-416.

Formula

G.f.: theta_3(q)^2*theta_3(q^5)^2, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 03 2018

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/12800) * 2^(1/5) * 5^(1/2) * Gamma(3/5)^4 * Gamma(7/10)^2 * (5+5^(1/2))^2 * (5^(1/2)+1)^4 / Pi / Gamma(3/4)^4 / Gamma(9/10)^2 = A388824. - Simon Plouffe, Sep 18 2025

Maple

See A236924.

Crossrefs

Sequence in context: A028658 A241535 A169784 * A351521 A028642 A159796

Adjacent sequences: A236926 A236927 A236928 * A236930 A236931 A236932

Keyword

nonn

Author

N. J. A. Sloane, Feb 15 2014

Status

approved