A320149 - OEIS

A320149

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

1, 2, 6, 12, 14, 24, 20, 16, 30, 14, 40, 60, 36, 72, 48, 16, 62, 36, 42, 108, 72, 96, 100, 48, 68, 42, 120, 120, 112, 168, 48, 64, 126, 40, 108, 192, 98, 216, 180, 48, 136, 84, 160, 252, 180, 168, 144, 96, 132, 114, 126, 216, 216, 312, 200, 80, 240, 72, 280, 348, 112

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OFFSET

0,2

COMMENTS

a(n) > 0 for n >= 0.

LINKS

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

Simon Plouffe, Numbers in the base e^Pi, arXiv:2509.15609 [math.NT], 2025. See p. 21/24, marked 214.

FORMULA

G.f.: theta_3(q) * theta_3(q^2)^3.

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = -(1/16) * Gamma(5/8)^4 * (3+2 * sqrt(2)) * (2+sqrt(2))^(1/2) / Pi / Gamma(7/8)^4 / (sqrt(2)-2) = A389052. - Simon Plouffe, Sep 22 2025

CROSSREFS

Cf. A320150, A236924, A320151, A320152, A320153.

Sequence in context: A057895 A111369 A190503 * A346305 A140760 A161922

Adjacent sequences: A320146 A320147 A320148 * A320150 A320151 A320152

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 06 2018

STATUS

approved