proposed

approved

editing

proposed

allocated for Ilya GutkovskiyExpansion 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

0,2

Number of nonnegative integer solutions to the equation x^2 + y^2 + 2*z^2 + 2*w^2 = n.

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

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 + ...

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]

Cf. A014110, A097057, A317645.

allocated

nonn

Ilya Gutkovskiy, Aug 02 2018

approved

editing

allocated for Ilya Gutkovskiy

allocated

approved