A033790 -id:A033790 - cp's OEIS frontend

A033782 Product t2(q^d); d | 23, where t2 = theta2(q)/(2*q^(1/4)).

1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 0

N. J. A. Sloane

nonn

Also the number of positive odd solutions to equation x^2 + 23y^2 = 8(n + 3). - Seiichi Manyama, May 21 2017

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

Cf. A035162, A128617, A033790.

Expansion of q^(-3) * (eta(q^2) * eta(q^46))^2 / (eta(q) * eta(q^23)) in powers of q. - Seiichi Manyama, May 21 2017

More terms from Seiichi Manyama, May 21 2017

A033806 Product t2(q^d); d | 47, where t2 = theta2(q)/(2*q^(1/4)).

Original entry on oeis.org

1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset: 0

N. J. A. Sloane

nonn

Also the number of positive odd solutions to equation x^2 + 47y^2 = 8(n + 6). - Seiichi Manyama, May 27 2017

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

Cf. A035162, A128617, A033782, A033790.

Expansion of q^(-6) * (eta(q^2) * eta(q^94))^2 / (eta(q) * eta(q^47)) in powers of q. - Seiichi Manyama, May 27 2017

More terms from Seiichi Manyama, May 27 2017

A287619 Number of positive odd solutions to equation x^2 + 39y^2 = 8*(n + 5).

Original entry on oeis.org

1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 0

Seiichi Manyama, May 28 2017

nonn

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

Cf. A035162, A128617.

Number of positive odd solutions to equation x^2 + (8*k - 1)*y^2 = 8*(n + k): A033782 (k=3), A033790 (k=4), this sequence (k=5), A033806 (k=6).

Expansion of q^(-5) * (eta(q^2) * eta(q^78))^2 / (eta(q) * eta(q^39)) in powers of q.

cp's OEIS Frontend

A033782 Product t2(q^d); d | 23, where t2 = theta2(q)/(2*q^(1/4)).

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A033806 Product t2(q^d); d | 47, where t2 = theta2(q)/(2*q^(1/4)).

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A287619 Number of positive odd solutions to equation x^2 + 39y^2 = 8*(n + 5).

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