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A317643
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Expansion of theta_3(q^3)*theta_3(q^4), where theta_3() is the Jacobi theta function.
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0
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1, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2
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OFFSET
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0,4
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COMMENTS
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Number of integer solutions to the equation 3*x^2 + 4*y^2 = n.
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1 + x^(6*k-3))^2*(1 - x^(6*k))*(1 + x^(8*k-4))^2*(1 - x^(8*k)).
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EXAMPLE
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G.f. = 1 + 2*q^3 + 2*q^4 + 4*q^7 + 2*q^12 + 6*q^16 + 4*q^19 + 2*q^27 + 4*q^28 + ...
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MATHEMATICA
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nmax = 100; CoefficientList[Series[EllipticTheta[3, 0, q^3] EllipticTheta[3, 0, q^4], {q, 0, nmax}], q]
nmax = 100; CoefficientList[Series[QPochhammer[-q^3, -q^3] QPochhammer[-q^4, -q^4]/(QPochhammer[q^3, -q^3] QPochhammer[q^4, -q^4]), {q, 0, nmax}], q]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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