A318187 Number of totally transitive rooted trees with n leaves.

2, 2, 4, 8, 16, 32, 62, 122, 234, 451, 857, 1630, 3068, 5772, 10778, 20093, 37259

Offset

1,1

Comments

A rooted tree is totally transitive if every branch of the root is totally transitive and every branch of a branch of the root is also a branch of the root.

Links

Table of n, a(n) for n=1..17.

Example

The a(5) = 16 totally transitive rooted trees with 5 leaves:
  (o(o)(o(o)(o)))
  (o(o)(o)(o(o)))
  (o(o)(o)(o)(o))
  (o(o)(oo(o)))
  (oo(o)(o(o)))
  (o(o)(o)(oo))
  (oo(o)(o)(o))
  (o(o)(ooo))
  (o(oo)(oo))
  (oo(o)(oo))
  (ooo(o)(o))
  (o(oooo))
  (oo(ooo))
  (ooo(oo))
  (oooo(o))
  (ooooo)

Mathematica

totralv[n_]:=totralv[n]=If[n==1, {{}, {{}}}, Join@@Table[Select[Union[Sort/@Tuples[totralv/@c]], Complement[Union@@#, #]=={}&], {c, Select[IntegerPartitions[n], Length[#]>1&]}]];
Table[Length[totralv[n]], {n, 8}]

Crossrefs

Cf. A000081, A000669, A001678, A004111, A050381, A279861, A290689, A290760, A290822, A318185, A318186.

Sequence in context: A171648 A189914 A286496 * A217931 A090129 A001137

Adjacent sequences: A318184 A318185 A318186 * A318188 A318189 A318190

Keyword

nonn,more

Author

Gus Wiseman, Aug 20 2018

Status

approved