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 A147817 Number of consistent sets of 4 irreflexive binary order relationships over n objects. 8
 186, 3050, 20790, 93030, 321580, 930636, 2362500, 5420580, 11473110, 22732710, 42628586, 76289850, 131160120, 217765240, 350657640, 549562536, 840752850, 1258681410, 1847900670, 2665301870, 3782707236, 5289850500, 7297782700, 9942741900, 13390527150 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS It seems that a(n) = A081064(n,4) = number of labeled acyclic directed graphs with n nodes and k = 4 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 4 arcs of the directed graph correspond to the 4-set of binary order relationships and they are consistent because the directed graph is acyclic. - Petros Hadjicostas, Apr 10 2020 LINKS Table of n, a(n) for n=4..28. V. I. Rodionov, On the number of labeled acyclic digraphs, Discr. Math. 105 (1-3) (1992), 319-321. FORMULA a(n) = binomial(n,4) * (n^4 + 2*n^3 - 5*n^2 - 22*n - 30). - Vaclav Kotesovec, Apr 11 2020 Conjectures from Colin Barker, Apr 11 2020: (Start) G.f.: 2*x^4*(93 + 688*x + 18*x^2 + 48*x^3 - 7*x^4) / (1 - x)^9. a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10. (End) MAPLE a := n -> (1/24)*(n-3)*(n-2)*(n-1)*n*(n*(n*(n*(n+2)-5)-22)-30): seq(a(n), n=4..28); # Peter Luschny, Apr 11 2020 MATHEMATICA Table[(1/24)*(n - 3)*(n - 2)*(n - 1)*n*(n*(n*(n*(n + 2) - 5) - 22) - 30), {n, 4, 25}] (* Wesley Ivan Hurt, Apr 12 2020 *) CROSSREFS Related sequences for the number of consistent sets of k irreflexive binary order relationships over n objects: A147796 (k = 3), A147821 (k = 5), A147860 (k = 6), A147872 (k = 7), A147881 (k = 8), A147883 (k = 9), A147964 (k = 10). Column k = 4 of A081064. Sequence in context: A251499 A251492 A289301 * A318270 A230898 A241942 Adjacent sequences: A147814 A147815 A147816 * A147818 A147819 A147820 KEYWORD nonn AUTHOR R. H. Hardin, May 04 2009 EXTENSIONS More terms from Vaclav Kotesovec, Apr 11 2020 Offset changed to n=4 by Petros Hadjicostas, Apr 11 2020 STATUS approved

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Last modified February 21 10:22 EST 2024. Contains 370228 sequences. (Running on oeis4.)