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A297662
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Number of chordless cycles in the complete tripartite graph K_n,n,n.
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0
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0, 3, 27, 108, 300, 675, 1323, 2352, 3888, 6075, 9075, 13068, 18252, 24843, 33075, 43200, 55488, 70227, 87723, 108300, 132300, 160083, 192027, 228528, 270000, 316875, 369603, 428652, 494508, 567675, 648675, 738048, 836352, 944163, 1062075, 1190700
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OFFSET
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1,2
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COMMENTS
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The only chordless cycles in a complete tripartite graph are cycles of length 4 confined to two of the partitions. - Andrew Howroyd, Jan 03 2018
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: -3*x^2*(1 + 4*x + x^2)/(-1 + x)^5.
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MATHEMATICA
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Table[3 Binomial[n, 2]^2, {n, 20}]
3 Binomial[Range[20], 2]^2
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 27, 108, 300}, 20]
SeriesCoefficient[Series[-3 x (1 + 4 x + x^2)/(-1 + x)^5, {x, 0, 20}], x]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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