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%I #25 Nov 30 2015 05:39:47
%S 1,2,2,6,6,4,12,4,2,14,0,8,18,4,12,16,6,4,14,8,12,24,12,8,12,10,0,18,
%T 12,12,36,12,2,16,12,8,42,12,12,36,0,12,0,8,24,28,24,8,18,14,14,32,12,
%U 12,48,8,12,36,0,16,48,12,12,28,6,16,36,16,12,32,24,24,14,8,0,42,24,8
%N Theta series of quadratic form with Gram matrix [ 1, 0, 0; 0, 2, 0; 0, 0, 3 ].
%C This is the digonal P lattice (the classical holotype) of dimension 3.
%H John Cannon, <a href="/A029594/b029594.txt">Table of n, a(n) for n = 0..10000</a>
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/digonalP.html">Home page for this lattice</a>
%F Euler transform of period 24 sequence [2, -1, 4, -4, 2, -4, 2, -2, 4, -1, 2, -5, 2, -1, 4, -2, 2, -4, 2, -4, 4, -1, 2, -3, ...]. - _Michael Somos_, Sep 20 2005
%F Expansion of eta(q^2)^3eta(q^4)^3eta(q^6)^5/(eta(q)eta(q^3)eta(q^8)eta(q^12))^2 in powers of q. - _Michael Somos_, Sep 20 2005
%F G.f.: theta_3(q)theta_3(q^2)theta_3(q^3).
%e 1 + 2*q + 2*q^2 + 6*q^3 + 6*q^4 + 4*q^5 + 12*q^6 + 4*q^7 + 2*q^8 + 14*q^9 + ...
%t s = EllipticTheta[3, 0, q] EllipticTheta[3, 0, q^2] EllipticTheta[3, 0, q^3] + O[q]^80; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 30 2015 *)
%o (PARI) a(n)=if(n<1, n==0, qfrep([1,0,0;0,2,0;0,0,3],n)[n]*2) /* _Michael Somos_, Sep 20 2005 */
%o (Sage)
%o Q = DiagonalQuadraticForm(ZZ, [1,3,2])
%o Q.representation_number_list(78) # _Peter Luschny_, Jun 25 2014
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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