A085628 Number of antisymmetric transitive binary relations on n labeled points.

1, 2, 12, 152, 3504, 135392, 8321472, 784621952, 110521185024, 22789653765632, 6769730814753792, 2859584874712881152, 1699286839524775931904, 1407801166901961190203392, 1613567168628788544015286272, 2541721059997800475952740401152, 5470980000021882982488097199161344

Offset: 0

Author

Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004

Keywords

• nonn

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..18
• G. Pfeiffer, Counting Transitive Relations, preprint, 2004.

Crossrefs

Cf. A079265 (unlabeled antisymmetric transitive relations), A001035 (labeled partial orders), A000798 (labeled reflexive transitive relations), A006905 (labeled transitive relations).

Programs

Mathematica

A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {, }][[All, 2]];
a[n_] := 2^n A001035[[n + 1]];
a /@ Range[0, 18] (* Jean-François Alcover, Jan 01 2020 *)

Formula

a(n) = 2^n * A001035(n) = A000079(n) * A001035(n)

E.g.f.: A(2*x) where A(x) is the e.g.f. for A001035. - Geoffrey Critzer, Jul 28 2014

Extensions

2 more terms from Charles R Greathouse IV, Aug 31 2006