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A318187 Number of totally transitive rooted trees with n leaves. 3
2, 2, 4, 8, 16, 32, 62, 122, 234, 451, 857, 1630, 3068, 5772, 10778, 20093, 37259 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 14:36 EDT 2019. Contains 328222 sequences. (Running on oeis4.)