A317645 Expansion of (1 + theta_3(q))^3*(1 + theta_3(q^2))/16, where theta_3() is the Jacobi theta function.

1, 3, 4, 4, 6, 7, 6, 6, 7, 9, 12, 10, 10, 15, 10, 6, 12, 15, 16, 18, 16, 16, 18, 12, 12, 18, 24, 22, 24, 25, 10, 18, 19, 18, 30, 26, 24, 33, 30, 12, 24, 27, 30, 36, 28, 31, 24, 24, 22, 33, 32, 30, 42, 43, 36, 24, 34, 24, 48, 46, 24, 51, 34, 30, 36, 30, 34, 54, 48, 42, 48, 30, 37, 45, 54, 38

Offset: 0

Author

Ilya Gutkovskiy, Aug 02 2018

Keywords

• nonn

Comments

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

Examples

			G.f. = 1 + 3*q + 4*q^2 + 4*q^3 + 6*q^4 + 7*q^5 + 6*q^6 + 6*q^7 + 7*q^8 + ...
		

Links

• Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Crossrefs

Cf. A014110, A156384, A236928.

Programs

Mathematica

nmax = 75; CoefficientList[Series[(1 + EllipticTheta[3, 0, q])^3 (1 + EllipticTheta[3, 0, q^2])/16, {q, 0, nmax}], q]
nmax = 75; CoefficientList[Series[(1 + QPochhammer[-q, -q]/QPochhammer[q, -q])^3 (1 + QPochhammer[-q^2, -q^2]/QPochhammer[q^2, -q^2])/16, {q, 0, nmax}], q]