A358454 Number of weakly transitive ordered rooted trees with n nodes.

1, 1, 1, 3, 6, 13, 33, 80, 201, 509, 1330, 3432, 8982, 23559, 62189

Offset: 1

Author

Gus Wiseman, Nov 18 2022

Keywords

• nonn
• more

Comments

We define an unlabeled ordered rooted tree to be weakly transitive if every branch of a branch of the root is itself a branch of the root.

Examples

			The a(1) = 1 through a(6) = 13 trees:
  o  (o)  (oo)  (ooo)   (oooo)   (ooooo)
                ((o)o)  ((o)oo)  ((o)ooo)
                (o(o))  ((oo)o)  ((oo)oo)
                        (o(o)o)  ((ooo)o)
                        (o(oo))  (o(o)oo)
                        (oo(o))  (o(oo)o)
                                 (o(ooo))
                                 (oo(o)o)
                                 (oo(oo))
                                 (ooo(o))
                                 ((o)(o)o)
                                 ((o)o(o))
                                 (o(o)(o))
		

Crossrefs

The unordered version is A290689, ranked by A290822.

The directed version is A358453.

A000081 counts rooted trees.

A306844 counts anti-transitive rooted trees.

Cf. A318185, A324695, A324751, A324756, A324758, A324764-A324768, A324838, A324840, A324844, A358456.

Programs

Mathematica

aot[n_]:=If[n==1,{{}},Join@@Table[Tuples[aot/@c],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n],Complement[Union@@#,#]=={}&]],{n,10}]