A033763 - OEIS

A033763

Product t2(q^d); d | 4, where t2 = theta2(q)/(2*q^(1/4)).

1, 1, 1, 2, 1, 2, 3, 3, 1, 2, 3, 1, 5, 3, 2, 4, 4, 3, 3, 3, 3, 5, 3, 2, 5, 5, 3, 8, 2, 2, 7, 4, 3, 6, 6, 4, 5, 3, 3, 5, 7, 3, 8, 4, 3, 10, 6, 6, 6, 4, 3, 5, 10, 2, 5, 7, 4, 10, 3, 4, 9, 9, 5, 8, 3, 4, 9, 7, 5, 9, 9, 5, 9, 5, 3, 10, 6, 4, 9, 5, 7, 9, 10, 5, 6, 7, 5

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OFFSET

0,4

COMMENTS

Also the number of positive odd solutions to equation a^2 + 2*b^2 + 4*c^2 = 8*n + 7. - Seiichi Manyama, May 29 2017

LINKS

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

FORMULA

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/64) * exp(7*Pi/8) * 2^(7/8) * Gamma(5/8)^3 * (1+sqrt(2)) / Pi^(3/4) / Gamma(7/8)^3 = A388395. - Simon Plouffe, Sep 15 2025

CROSSREFS

Sequence in context: A117127 A278148 A136624 * A033803 A035531 A118977

Adjacent sequences: A033760 A033761 A033762 * A033764 A033765 A033766

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Seiichi Manyama, May 22 2017

STATUS

approved