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A317641 Expansion of theta_3(q)*theta_3(q^10), where theta_3() is the Jacobi theta function. 1

%I

%S 1,2,0,0,2,0,0,0,0,2,2,4,0,0,4,0,2,0,0,4,0,0,0,0,0,2,4,0,0,0,0,0,0,0,

%T 0,4,2,0,0,0,2,4,0,0,4,0,4,0,0,6,0,0,0,0,0,0,4,0,0,4,0,0,0,0,2,4,0,0,

%U 0,0,0,0,0,0,4,0,4,0,0,0,0,2,0,0,0,0,0,0,0,4,2,8,0,0,4,0,0,0,0,4,2

%N Expansion of theta_3(q)*theta_3(q^10), where theta_3() is the Jacobi theta function.

%C Number of integer solutions to the equation x^2 + 10*y^2 = n.

%H Seiichi Manyama, <a href="/A317641/b317641.txt">Table of n, a(n) for n = 0..10000</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%F G.f.: Product_{k>=1} (1 + x^(2*k-1))^2*(1 - x^(2*k))*(1 + x^(20*k-10))^2*(1 - x^(20*k)).

%e G.f. = 1 + 2*q + 2*q^4 + 2*q^9 + 2*q^10 + 4*q^11 + 4*q^14 + 2*q^16 + 4*q^19 + ...

%t nmax = 100; CoefficientList[Series[EllipticTheta[3, 0, q] EllipticTheta[3, 0, q^10], {q, 0, nmax}], q]

%t nmax = 100; CoefficientList[Series[QPochhammer[-q, -q] QPochhammer[-q^10, -q^10]/(QPochhammer[q, -q] QPochhammer[q^10, -q^10]), {q, 0, nmax}], q]

%Y Cf. A000024, A020673, A033201, A033723, A216577, A216579, A258034.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Aug 02 2018

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Last modified June 25 18:30 EDT 2019. Contains 324353 sequences. (Running on oeis4.)