A296105 a(n) is the number of connected transitive relations over n unlabeled nodes.

1, 2, 5, 25, 157, 1325, 14358, 199763, 3549001, 80673244, 2352747542, 88240542454, 4261209044877, 264988507673267, 21207485269909946, 2182146922863398203

Offset

0,2

Comments

Inverse Euler transform of A091073. Here "connected" means that it is possible to reach any vertex starting from any other vertex by traversing edges in some direction, i.e., not necessarily in the direction in which the edges point, as in weakly connected digraphs.

Links

Table of n, a(n) for n=0..15.

Example

a(2) = 5 because there are five connected transitive relations up to isomorphism: a->b with no loops, a->b with a loop on a, a->b with a loop on b, a->b->a with no loops, and a->b->a with loops on both a and b.

Mathematica

A091073 = Cases[Import["https://oeis.org/A091073/b091073.txt", "Table"], {_, _}][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A091073 // Rest] (* Jean-François Alcover, Dec 29 2019, updated Mar 17 2020 *)

Crossrefs

Cf. A091073 (all unlabeled transitive relations). For the labeled case, see A245731 (connected labeled transitive relations) and A006905 (all labeled transitive relations).

Sequence in context: A329158 A337435 A074417 * A268120 A324263 A049650

Adjacent sequences: A296102 A296103 A296104 * A296106 A296107 A296108

Keyword

nonn,more

Author

Daniele P. Morelli, Dec 04 2017

Status

approved