The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A318185 Number of totally transitive rooted trees with n nodes. 14
 1, 1, 1, 2, 3, 5, 7, 12, 17, 28, 41, 65, 96, 150, 221, 342, 506, 771, 1142, 1731, 2561, 3855, 5702, 8538, 12620, 18817, 27774, 41276, 60850, 90139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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. Unlike transitive rooted trees (A290689), every terminal subtree of a totally transitive rooted tree is itself totally transitive. LINKS EXAMPLE The a(8) = 12 totally transitive rooted trees:   (o(o)(o(o)))   (o(o)(o)(o))   (o(o)(ooo))   (o(oo)(oo))   (oo(o)(oo))   (ooo(o)(o))   (o(ooooo))   (oo(oooo))   (ooo(ooo))   (oooo(oo))   (ooooo(o))   (ooooooo) The a(9) = 17 totally transitive rooted trees:   (o(o)(oo(o)))   (oo(o)(o(o)))   (o(o)(o)(oo))   (oo(o)(o)(o))   (o(o)(oooo))   (o(oo)(ooo))   (oo(o)(ooo))   (oo(oo)(oo))   (ooo(o)(oo))   (oooo(o)(o))   (o(oooooo))   (oo(ooooo))   (ooo(oooo))   (oooo(ooo))   (ooooo(oo))   (oooooo(o))   (oooooooo) MATHEMATICA totra[n_]:=totra[n]=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[totra/@c]], Complement[Union@@#, #]=={}&], {c, IntegerPartitions[n-1]}]]; Table[Length[totra[n]], {n, 20}] CROSSREFS Cf. A000081, A001678, A004111, A279861, A290689, A290760, A290822, A318186, A318187. Sequence in context: A326593 A123569 A305651 * A048816 A080528 A245152 Adjacent sequences:  A318182 A318183 A318184 * A318186 A318187 A318188 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 20 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 13:56 EDT 2021. Contains 343204 sequences. (Running on oeis4.)