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 A147821 Number of consistent sets of 5 irreflexive binary order relationships over n objects. 8
 108, 6180, 83952, 601944, 2991576, 11662056, 38167920, 109368864, 282174948, 668565612, 1475938464, 3069513720, 6065522736, 11466274512, 20850952608, 36639176832, 62447999580, 103567126068, 167581781136, 265177823064, 411169457160, 625796259000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS It seems that a(n) = A081064(n,5) is the number of labeled acyclic directed graphs with n nodes and k = 5 arcs (see Rodionov (1992)). The reason is that we may label the graphs with the n objects and draw an arc from X towards Y if and only if X < Y. The 5 arcs of the directed graph correspond to the 3-set of binary order relationships and they are consistent because the directed graph is acyclic. - Petros Hadjicostas, Apr 10 2020 LINKS V. I. Rodionov, On the number of labeled acyclic digraphs, Discr. Math. 105 (1-3) (1992), 319-321. FORMULA a(n) = (n-3)*(n-2)*(n-1)*n*(n^6 + n^5 - 15*n^4 - 45*n^3 - 4*n^2 + 326*n + 900)/120. - Vaclav Kotesovec, Apr 11 2020 Conjectures from Colin Barker, Apr 11 2020: (Start) G.f.: 12*x^4*(9 + 416*x + 1826*x^2 + 46*x^3 + 291*x^4 - 78*x^5 + 10*x^6) / (1 - x)^11. a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>12. (End) MAPLE a := n -> (1/120)*(n-3)*(n-2)*(n-1)*n*(n*(n*(n*(n*(n^2+n-15)-45)-4)+326)+900): seq(a(n), n=4..25); # Peter Luschny, Apr 11 2020 MATHEMATICA Table[(n - 3)*(n - 2)*(n - 1)*n*(n^6 + n^5 - 15*n^4 - 45*n^3 - 4*n^2 + 326*n + 900)/120, {n, 4, 25}] (* Wesley Ivan Hurt, Apr 11 2020 *) CROSSREFS Related sequences for the number of consistent sets of k irreflexive binary order relationships over n objects: A147796 (k = 3), A147817 (k = 4), A147860 (k = 6), A147872 (k = 7), A147881 (k = 8), A147883 (k = 9), A147964 (k = 10). Column k = 5 of A081064. Sequence in context: A138784 A035812 A054624 * A269148 A143403 A269210 Adjacent sequences: A147818 A147819 A147820 * A147822 A147823 A147824 KEYWORD nonn,easy AUTHOR R. H. Hardin, May 04 2009 EXTENSIONS More terms from Vaclav Kotesovec, Apr 11 2020 Offset changed by Petros Hadjicostas, Apr 11 2020 STATUS approved

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Last modified March 31 03:22 EDT 2023. Contains 361626 sequences. (Running on oeis4.)