%I #20 Oct 14 2018 08:21:54
%S 1,2,0,0,2,0,2,4,0,2,4,0,0,0,0,4,2,0,0,0,0,0,4,0,2,6,0,0,4,0,0,4,0,4,
%T 0,0,2,0,0,0,4,0,4,0,0,0,0,0,0,6,0,0,0,0,2,8,0,0,4,0,4,0,0,4,2,0,0,0,
%U 0,0,8,0,0,4,0,0,0,0,0,4,0,2,0,0,0,0,0,4,4,0,4,0,0
%N Coefficients in expansion of theta_3(q) * theta_3(q^6) in powers of q.
%C Number of representations of n as a sum of six times a square and a square. - _Ralf Stephan_, May 14 2007
%C a(n) < 2 if and only if n is in A002480. a(n) > 0 if and only if n is in A002481. - _Michael Somos_, Mar 01 2011
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
%H Seiichi Manyama, <a href="/A046113/b046113.txt">Table of n, a(n) for n = 0..10000</a>
%H A. Berkovich and H. Yesilyurt, <a href="http://arXiv.org/abs/math.NT/0611300">Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms</a>
%F G.f.: Sum_{ i, j = -inf .. inf } q^(i^2 + 6*j^2).
%F a(n) = A000377(n) + A115660(n). - _Michael Somos_, Mar 01 2011
%e G.f. = 1 + 2*x + 2*x^4 + 2*x^6 + 4*x^7 + 2*x^9 + 4*x^10 + 4*x^15 + 2*x^16 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^6], {q, 0, n}]; (* _Michael Somos_, Apr 19 2015 *)
%o (PARI) {a(n) = my(G); if( n<0, 0, G = [ 1, 0; 0, 6]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n)), n))}; /* _Michael Somos_, Mar 01 2011 */
%Y Cf. A000377, A002480, A002481, A115660.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 18 2002