A317641 Expansion of theta_3(q)*theta_3(q^10), where theta_3() is the Jacobi theta function.

1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 4, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 8, 0, 0, 4, 0, 0, 0, 0, 4, 2

Offset: 0

Author

Ilya Gutkovskiy, Aug 02 2018

Keywords

• nonn

Comments

Number of integer solutions to the equation x^2 + 10*y^2 = n.

Examples

			G.f. = 1 + 2*q + 2*q^4 + 2*q^9 + 2*q^10 + 4*q^11 + 4*q^14 + 2*q^16 + 4*q^19 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Crossrefs

Cf. A000024, A020673, A033201, A033723, A216577, A216579, A258034.

Programs

Mathematica

nmax = 100; CoefficientList[Series[EllipticTheta[3, 0, q] EllipticTheta[3, 0, q^10], {q, 0, nmax}], q]
nmax = 100; CoefficientList[Series[QPochhammer[-q, -q] QPochhammer[-q^10, -q^10]/(QPochhammer[q, -q] QPochhammer[q^10, -q^10]), {q, 0, nmax}], q]

Formula

G.f.: Product_{k>=1} (1 + x^(2*k-1))^2*(1 - x^(2*k))*(1 + x^(20*k-10))^2*(1 - x^(20*k)).