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%I #31 Jun 24 2018 16:04:08
%S 0,0,9,2,91,2022,9,738,43315,2679246,30,5613,950062,174184755,
%T 33887517990,91,43404,21480921,11765865678,6862930841141,
%U 4169289730628814,258,338259,497812638,816999710223,1429469771994078,2605213713043722909,4883659745750360600262,729,2679228,11765822365,57906482267826,303941554100145501
%N Triangle read by rows, 1 <= k <= n: T(n,k) = non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry.
%C Colors are not being permuted, i.e., Power Group Enumeration does not apply here.
%D F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2506511/">Burnside lemma and translational symmetries of the torus.</a>
%F T(n,k) = (Q!/(n*k))*(Sum_{d|n} Sum_{f|k} phi(d) phi(f) S(gcd(d,f)*(n/d)*(k/f), Q)) with Q=3 and S(n,k) Stirling numbers of the second kind.
%Y Cf. A184284, A294684, A294686, A294687, A294791, A294792, A294793, A294794. T(n,1) is A056283.
%K nonn,tabl,nice
%O 1,3
%A _Marko Riedel_, Nov 06 2017
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