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

0,2

Comments

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

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

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)).

Example

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 + ...

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]

Crossrefs

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

Sequence in context: A138811 A107494 A079205 * A107497 A000095 A258322

Adjacent sequences: A317638 A317639 A317640 * A317642 A317643 A317644

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2018

Status

approved