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-François 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
KEYWORD
nonn
AUTHOR
STATUS
approved