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%I #14 Sep 08 2022 08:44:35
%S 1,42,210,350,882,1050,1750,2100,3570,3066,5250,5124,7350,7350,10500,
%T 8064,14322,12600,15330,15750,22050,16814,25620,22260,29750,25242,
%U 36750,28700,44100,35364,40320,42000,57330,42700,63000,50442,64386,57540,78750,56448
%N Theta series of A_6 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A6.html">Home page for this lattice</a>
%e 1 + 42*q^2 + 210*q^4 + 350*q^6 + 882*q^8 + 1050*q^10 + 1750*q^12 + 2100*q^14 + 3570*q^16 + 3066*q^18 + 5250*q^20 + 5124*q^22 + 7350*q^24 + 7350*q^26 + 10500*q^28 + 8064*q^30 + 14322*q^32 + 12600*q^34 + 15330*q^36 + 15750*q^38 + 22050*q^40 + 16814*q^42 + 25620*q^44 + ...
%t terms = 40; f[q_] = LatticeData["A6", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; DeleteCases[CoefficientList[s, q^(1/2) ] // Round, 0][[1 ;; terms]] (* _Jean-François Alcover_, Jul 04 2017 *)
%o (Magma) L:=Lattice("A",6); T1<q> := ThetaSeries(L,120);
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_