OFFSET
0,2
COMMENTS
Number of nonnegative integer solutions to the equation x^2 + y^2 + z^2 + 2*w^2 = n.
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2018
STATUS
approved