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 A297662 Number of chordless cycles in the complete tripartite graph K_n,n,n. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Eric Weisstein's World of Mathematics, Chordless Cycle Eric Weisstein's World of Mathematics, Complete Tripartite Graph Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1). FORMULA a(n) = 3*n^2*(n-1)^2/4 = 3*A000537(n). - Andrew Howroyd, Jan 03 2018 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. MATHEMATICA 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] PROG (PARI) a(n) = 3*n^2*(n-1)^2/4; \\ Andrew Howroyd, Jan 03 2018 CROSSREFS Cf. A000537, A234616. Sequence in context: A303407 A173491 A195799 * A127210 A161807 A261716 Adjacent sequences:  A297659 A297660 A297661 * A297663 A297664 A297665 KEYWORD nonn AUTHOR Eric W. Weisstein, Jan 02 2018 EXTENSIONS a(6)-a(36) from Andrew Howroyd, Jan 03 2018 STATUS approved

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Last modified June 28 12:59 EDT 2022. Contains 354907 sequences. (Running on oeis4.)