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

Author

Gus Wiseman, Aug 20 2018

Keywords

• nonn
• more

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.

Examples

			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)
		

Crossrefs

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

Programs

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}]