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A294687
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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.
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7
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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
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OFFSET
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1,5
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COMMENTS
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Colors are not being permuted, i.e., Power Group Enumeration does not apply here.
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REFERENCES
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F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
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LINKS
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FORMULA
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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.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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