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%I #30 Jun 24 2018 16:04:18
%S 0,0,6,0,260,20720,6,5112,1223136,257706024,48,81876,67769552,
%T 54278580036,44900438149488,260,1223396,3731753700,11681058472672,
%U 38403264917970196,131160169581733489616,1200,17815020,207438938000,2570217454576416,33725471278376393424,460532748521625850986660,6467585568566200114362823920,5106,257706012,11681057249536,576229125971686224
%N Triangle read by rows, 1 <= k <= n: T(n,k) = non-isomorphic colorings of a toroidal n X k grid using exactly four 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=4 and S(n,k) Stirling numbers of the second kind.
%Y Cf. A294684, A294685, A294687, A294791, A294792, A294793, A294794. T(n,1) is A056284.
%K nonn,tabl,nice
%O 1,3
%A _Marko Riedel_, Nov 06 2017
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