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A080918 Number of integer solutions to the equation 2x^2+y^2+32z^2=n. 5


%S 1,2,2,4,2,0,4,0,2,6,0,4,4,0,0,0,2,4,6,4,0,0,4,0,4,2,0,8,0,0,0,0,4,12,

%T 8,8,10,0,12,0,4,16,0,12,12,0,0,0,8,10,14,16,0,0,16,0,8,12,0,20,0,0,0,

%U 0,6,16,16,4,16,0,8,0,6,12,0,12,12,0,0,0,8,14,8,20,0,0,20,0,4,20,0,8,0

%N Number of integer solutions to the equation 2x^2+y^2+32z^2=n.

%H Seiichi Manyama, <a href="/A080918/b080918.txt">Table of n, a(n) for n = 0..10000</a>

%H J. B. Tunnell, <a href="http://dx.doi.org/10.1007/BF01389327">A classical Diophantine problem and modular forms of weight 3/2</a>, Invent. Math., 72 (1983), 323-334.

%F G.f.: theta_3(q) * theta_3(q^2) * theta_3(q^32).

%o (PARI) {a(n)=my(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3*eta(x^4+A)^3*eta(x^64+A)^5/ (eta(x+A)*eta(x^8+A)*eta(x^32+A)*eta(x^128+A))^2, n))}

%Y a(2n-1)=A072069(n).

%Y Cf. A000122 (theta_3(q)), A080917.

%K nonn

%O 0,2

%A _Michael Somos_, Feb 23 2003

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Last modified May 29 15:44 EDT 2020. Contains 334704 sequences. (Running on oeis4.)