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 A294687 Triangle read by rows, 1 <= k <= n: T(n,k) = non-isomorphic colorings of a toroidal n X k grid using exactly five colors under translational symmetry. 7
 0, 0, 0, 0, 300, 92680, 0, 15750, 13794150, 8221452750, 24, 510312, 1686135376, 4495236798162, 11696087875731720, 300, 13794450, 193054017440, 2425003938178050, 30852000867277668428, 403564024914127655401650, 2400, 343501500, 21664357535320, 1317601563731383350, 82985159653854019928352, 5411356249329837891442095560 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Colors are not being permuted, i.e., Power Group Enumeration does not apply here. REFERENCES F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973. LINKS Table of n, a(n) for n=1..27. Marko Riedel et al., Burnside lemma and translational symmetries of the torus. FORMULA 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=5 and S(n,k) Stirling numbers of the second kind. CROSSREFS Cf. A294684, A294685, A294686, A294791, A294792, A294793, A294794. T(n,1) is A056285. Sequence in context: A223350 A190880 A063935 * A015275 A051306 A151609 Adjacent sequences: A294684 A294685 A294686 * A294688 A294689 A294690 KEYWORD nonn,tabl,nice AUTHOR Marko Riedel, Nov 06 2017 STATUS approved

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Last modified May 26 08:28 EDT 2024. Contains 372813 sequences. (Running on oeis4.)