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URL: https://oeis.org/A320151

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A320151
Number of integer solutions to a^2 + 2*b^2 + 2*c^2 + 5*d^2 = n.
8
1, 2, 4, 8, 6, 10, 12, 8, 28, 22, 24, 40, 8, 32, 36, 16, 54, 32, 28, 56, 26, 32, 48, 40, 84, 74, 72, 48, 24, 92, 52, 96, 92, 32, 96, 80, 42, 64, 80, 80, 168, 124, 48, 72, 72, 94, 132, 104, 72, 126, 124, 96, 48, 96, 120, 168, 252, 96, 120, 168, 48, 196, 128, 88, 246
OFFSET
0,2
COMMENTS
a(n) > 0 for n >= 0.
LINKS
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)^2 * theta_3(q^5).
Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/25600) * 5^(3/4) * Gamma(5/8)^4 * (3+2 * sqrt(2)) * sqrt(2) * (5-5^(1/2))^(3/2) * (4+2 * sqrt(2)) * (5^(1/2)+1)^3 / Pi / Gamma(7/8)^4 = A389054. - Simon Plouffe, Sep 22 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 06 2018
STATUS
approved