A317646 Expansion of (1 + theta_3(q))^2*(1 + theta_3(q^2))^2/16, where theta_3() is the Jacobi theta function.
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
Offset: 0
Keywords
Examples
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 + ...
Links
- Eric Weisstein's World of Mathematics, Jacobi Theta Functions
Programs
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Mathematica
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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