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A294685
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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 three colors under translational symmetry.
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7
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0, 0, 9, 2, 91, 2022, 9, 738, 43315, 2679246, 30, 5613, 950062, 174184755, 33887517990, 91, 43404, 21480921, 11765865678, 6862930841141, 4169289730628814, 258, 338259, 497812638, 816999710223, 1429469771994078, 2605213713043722909, 4883659745750360600262, 729, 2679228, 11765822365, 57906482267826, 303941554100145501
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OFFSET
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1,3
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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=3 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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