|
|
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
|
|
|
FORMULA
|
a(n) = binomial(n,4) * (n^4 + 2*n^3 - 5*n^2 - 22*n - 30). - Vaclav Kotesovec, Apr 11 2020
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):
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|