A147821 Number of consistent sets of 5 irreflexive binary order relationships over n objects.

108, 6180, 83952, 601944, 2991576, 11662056, 38167920, 109368864, 282174948, 668565612, 1475938464, 3069513720, 6065522736, 11466274512, 20850952608, 36639176832, 62447999580, 103567126068, 167581781136, 265177823064, 411169457160, 625796259000

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

Table of n, a(n) for n=4..25.

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