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Number of positive odd solutions to equation x^2 + 39y^2 = 8*(n + 5).
1

%I #13 May 28 2017 10:33:52

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0

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

%H Seiichi Manyama, <a href="/A287619/b287619.txt">Table of n, a(n) for n = 0..10000</a>

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

%Y Cf. A035162, A128617.

%Y 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).

%K nonn

%O 0,46

%A _Seiichi Manyama_, May 28 2017