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A317646
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Expansion of (1 + theta_3(q))^2*(1 + theta_3(q^2))^2/16, where theta_3() is the Jacobi theta function.
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0
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1, 2, 3, 4, 5, 4, 5, 4, 5, 8, 8, 8, 11, 8, 6, 8, 5, 10, 14, 12, 16, 12, 11, 8, 11, 14, 14, 20, 18, 12, 14, 12, 5, 20, 19, 20, 30, 16, 17, 16, 16, 18, 24, 20, 25, 28, 14, 16, 11, 22, 25, 28, 34, 20, 30, 24, 18, 28, 26, 28, 42, 24, 20, 32, 5, 28, 36, 28, 41, 32, 32, 20, 30, 30, 28, 44
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OFFSET
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0,2
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COMMENTS
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Number of nonnegative integer solutions to the equation x^2 + y^2 + 2*z^2 + 2*w^2 = n.
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LINKS
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EXAMPLE
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G.f. = 1 + 2*q + 3*q^2 + 4*q^3 + 5*q^4 + 4*q^5 + 5*q^6 + 4*q^7 + 5*q^8 + ...
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MATHEMATICA
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nmax = 75; CoefficientList[Series[(1 + EllipticTheta[3, 0, q])^2 (1 + EllipticTheta[3, 0, q^2])^2/16, {q, 0, nmax}], q]
nmax = 75; CoefficientList[Series[(1 + QPochhammer[-q, -q]/QPochhammer[q, -q])^2 (1 + QPochhammer[-q^2, -q^2]/QPochhammer[q^2, -q^2])^2/16, {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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