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A296546
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Triangle read by rows T(n,k): number of undirected cycles of length k in the complete tripartite graph K_{n,n,n} (n = 1...; k = 3..3n)
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1
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1, 8, 15, 24, 16, 27, 108, 324, 774, 1620, 2268, 1584, 64, 396, 1728, 7200, 27648, 87480, 232704, 476928, 663552, 463104, 125, 1050, 6000, 35800, 198000, 977400, 4392000, 17068320, 56376000, 151632000, 311040000, 430272000, 299289600
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OFFSET
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1,2
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LINKS
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FORMULA
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Row sums of T(n,k) give A234616(n).
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EXAMPLE
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Written as cycle polynomials:
x^3
8 x^3 + 15 x^4 + 24 x^5 + 16 x^6
27 x^3 + 108 x^4 + 324 x^5 + 774 x^6 + 1620 x^7 + 2268 x^8 + 1584 x^9
64 x^3 + 396 x^4 + 1728 x^5 + 7200 x^6 + 27648 x^7 + 87480 x^8 + 232704 x^9 + 476928 x^10 + 663552 x^11 + 463104 x^12
giving the array
1
8, 15, 24, 16
27, 108, 324, 774, 1620, 2268, 1584
64, 396, 1728, 7200, 27648, 87480, 232704, 476928, 663552, 463104
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MATHEMATICA
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Table[Tally[Length /@ FindCycle[CompleteGraph[{n, n, n}], Infinity, All]][[All, 2]], {n, 4}] // Flatten
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CROSSREFS
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Cf. A234616 (number of undirected cycles in K_{n,n,n}).
Cf. A144151 (cycle polynomial coefficients of complete graph K_n).
Cf. A291909 (cycle polynomial coefficients of complete bipartite graph K_{n,n}).
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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