

A317645


Expansion of (1 + theta_3(q))^3*(1 + theta_3(q^2))/16, where theta_3() is the Jacobi theta function.


1



1, 3, 4, 4, 6, 7, 6, 6, 7, 9, 12, 10, 10, 15, 10, 6, 12, 15, 16, 18, 16, 16, 18, 12, 12, 18, 24, 22, 24, 25, 10, 18, 19, 18, 30, 26, 24, 33, 30, 12, 24, 27, 30, 36, 28, 31, 24, 24, 22, 33, 32, 30, 42, 43, 36, 24, 34, 24, 48, 46, 24, 51, 34, 30, 36, 30, 34, 54, 48, 42, 48, 30, 37, 45, 54, 38
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OFFSET

0,2


COMMENTS

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


LINKS

Table of n, a(n) for n=0..75.
Eric Weisstein's World of Mathematics, Jacobi Theta Functions


EXAMPLE

G.f. = 1 + 3*q + 4*q^2 + 4*q^3 + 6*q^4 + 7*q^5 + 6*q^6 + 6*q^7 + 7*q^8 + ...


MATHEMATICA

nmax = 75; CoefficientList[Series[(1 + EllipticTheta[3, 0, q])^3 (1 + EllipticTheta[3, 0, q^2])/16, {q, 0, nmax}], q]
nmax = 75; CoefficientList[Series[(1 + QPochhammer[q, q]/QPochhammer[q, q])^3 (1 + QPochhammer[q^2, q^2]/QPochhammer[q^2, q^2])/16, {q, 0, nmax}], q]


CROSSREFS

Cf. A014110, A156384, A236928.
Sequence in context: A277193 A240728 A164326 * A117571 A008474 A111611
Adjacent sequences: A317642 A317643 A317644 * A317646 A317647 A317648


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Aug 02 2018


STATUS

approved



