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A317642 Expansion of theta_3(q^2)*theta_3(q^5), where theta_3() is the Jacobi theta function. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A291900 A263146 A028959 * A258762 A079181 A093693

Adjacent sequences:  A317639 A317640 A317641 * A317643 A317644 A317645

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 02 2018

STATUS

approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)