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A034933 Expansion of theta_3(q)^2 * theta_3(q^3) in powers of q. 8
1, 4, 4, 2, 12, 16, 0, 8, 20, 4, 8, 8, 10, 32, 8, 0, 28, 24, 4, 8, 32, 16, 16, 16, 0, 28, 8, 2, 40, 48, 8, 8, 52, 0, 8, 16, 12, 64, 16, 8, 40, 24, 0, 24, 40, 16, 16, 16, 26, 28, 20, 0, 64, 80, 0, 16, 40, 24, 24, 8, 0, 64, 24, 8, 60, 48, 8, 24, 72, 0, 16, 16, 20, 48, 24, 10, 40, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=0 if n == 6*9^k (mod 9^(k+1)) for some k>=0. - Robert Israel, Aug 11 2019

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

Number of integer solutions to x^2 + y^2 + 3*z^2 = n.

Euler transform of period 12 sequence [4, -6, 6, -2, 4, -9, 4, -2, 6, -6, 4, -3, ...]. - Michael Somos, Sep 21 2005

Expansion of (eta(q^2)^2 * eta(q^6))^5 / (eta(q)^2 * eta(q^3) * eta(q^4)^2 * eta(q^12))^2 in power of q. - Michael Somos, Sep 21 2005

G.f.: theta_3(q)^2 * theta_3(q^3).

EXAMPLE

1 + 4*q + 4*q^2 + 2*q^3 + 12*q^4 + 16*q^5 + 8*q^7 + 20*q^8 + 4*q^9 +...

MAPLE

S:= series(JacobiTheta3(0, q)^2*JacobiTheta3(0, q^3), q, 101):

seq(coeff(S, q, i), i=0..100); # Robert Israel, Aug 11 2019

MATHEMATICA

CoefficientList[EllipticTheta[3, 0, q]^2*EllipticTheta[3, 0, q^3]+O[q]^80, q] (* Jean-Fran├žois Alcover, Nov 27 2015 *)

PROG

(PARI) {a(n) = if( n<1, n==0, qfrep( [ 1, 0, 0; 0, 1, 0; 0, 0, 3], n)[n] * 2)} /* Michael Somos, Sep 21 2005 */

CROSSREFS

Sequence in context: A202322 A232523 A224821 * A320148 A320147 A272364

Adjacent sequences:  A034930 A034931 A034932 * A034934 A034935 A034936

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)