A034933 Expansion of theta_3(q)^2 * theta_3(q^3) in powers of q.
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
Offset: 0
Keywords
Examples
1 + 4*q + 4*q^2 + 2*q^3 + 12*q^4 + 16*q^5 + 8*q^7 + 20*q^8 + 4*q^9 +...
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
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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
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Mathematica
CoefficientList[EllipticTheta[3, 0, q]^2*EllipticTheta[3, 0, q^3]+O[q]^80, q] (* Jean-François Alcover, Nov 27 2015 *)
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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 */
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).
Comments