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

0,2

Comments

Number of nonnegative integer solutions to the equation x^2 + y^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 + 3*q + 4*q^2 + 4*q^3 + 6*q^4 + 7*q^5 + 6*q^6 + 6*q^7 + 7*q^8 + ...

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]

Crossrefs

Cf. A014110, A156384, A236928.

Sequence in context: A277193 A240728 A164326 * A117571 A008474 A349215

Adjacent sequences: A317642 A317643 A317644 * A317646 A317647 A317648

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2018

Status

approved