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A294686
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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 four colors under translational symmetry.
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7
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0, 0, 6, 0, 260, 20720, 6, 5112, 1223136, 257706024, 48, 81876, 67769552, 54278580036, 44900438149488, 260, 1223396, 3731753700, 11681058472672, 38403264917970196, 131160169581733489616, 1200, 17815020, 207438938000, 2570217454576416, 33725471278376393424, 460532748521625850986660, 6467585568566200114362823920, 5106, 257706012, 11681057249536, 576229125971686224
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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=4 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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