A317642 Expansion of theta_3(q^2)*theta_3(q^5), where theta_3() is the Jacobi theta function.

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

Offset

0,3

Comments

Number of integer solutions to the equation 2*x^2 + 5*y^2 = n.

Links

Table of n, a(n) for n=0..98.

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

Formula

G.f.: Product_{k>=1} (1 + x^(4*k-2))^2*(1 - x^(4*k))*(1 + x^(10*k-5))^2*(1 - x^(10*k)).

Example

G.f. = 1 + 2*q^2 + 2*q^5 + 4*q^7 + 2*q^8 + 4*q^13 + 2*q^18 + 2*q^20 + 4*q^22 + ...

Mathematica

nmax = 98; CoefficientList[Series[EllipticTheta[3, 0, q^2] EllipticTheta[3, 0, q^5], {q, 0, nmax}], q]
nmax = 98; CoefficientList[Series[QPochhammer[-q^2, -q^2] QPochhammer[-q^5, -q^5]/(QPochhammer[q^2, -q^2] QPochhammer[q^5, -q^5]), {q, 0, nmax}], q]

Crossrefs

Cf. A000286, A020674, A033718, A106889, A108563, A192323.

Sequence in context: A365047 A361015 A028959 * A258762 A079181 A093693

Adjacent sequences: A317639 A317640 A317641 * A317643 A317644 A317645

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2018

Status

approved