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A317643 Expansion of theta_3(q^3)*theta_3(q^4), where theta_3() is the Jacobi theta function. 0
1, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of integer solutions to the equation 3*x^2 + 4*y^2 = n.

LINKS

Table of n, a(n) for n=0..100.

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^(6*k-3))^2*(1 - x^(6*k))*(1 + x^(8*k-4))^2*(1 - x^(8*k)).

EXAMPLE

G.f. = 1 + 2*q^3 + 2*q^4 + 4*q^7 + 2*q^12 + 6*q^16 + 4*q^19 + 2*q^27 + 4*q^28 + ...

MATHEMATICA

nmax = 100; CoefficientList[Series[EllipticTheta[3, 0, q^3] EllipticTheta[3, 0, q^4], {q, 0, nmax}], q]

nmax = 100; CoefficientList[Series[QPochhammer[-q^3, -q^3] QPochhammer[-q^4, -q^4]/(QPochhammer[q^3, -q^3] QPochhammer[q^4, -q^4]), {q, 0, nmax}], q]

CROSSREFS

Cf. A000049, A020677, A068229, A108563, A192323.

Sequence in context: A254040 A062275 A138270 * A179011 A300465 A300646

Adjacent sequences:  A317640 A317641 A317642 * A317644 A317645 A317646

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 02 2018

STATUS

approved

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)