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A317641 Expansion of theta_3(q)*theta_3(q^10), where theta_3() is the Jacobi theta function. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)