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

0,2

Comments

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

Links

Table of n, a(n) for n=0..75.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Example

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 + ...

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]

Crossrefs

Cf. A014110, A097057, A317645.

Sequence in context: A305901 A291520 A354445 * A305748 A302981 A205785

Adjacent sequences: A317643 A317644 A317645 * A317647 A317648 A317649

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2018

Status

approved