A290689 Number of transitive rooted trees with n nodes.

1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 88, 143, 229, 370, 592, 955, 1527, 2457, 3929, 6304, 10081

Offset

1,4

Comments

A rooted tree is transitive if every proper terminal subtree is also a branch of the root. First differs from A206139 at a(13) = 143.

Links

Table of n, a(n) for n=1..22.

Robert P. P. McKone, The transitive rooted tree with n=1 to n=22 nodes.

Example

The a(7) = 8 trees are: (o(oooo)), (oo(ooo)), (o(o)((o))), (o(o)(oo)), (ooo(oo)), (oo(o)(o)), (oooo(o)), (oooooo).

Mathematica

nn=18;
rtall[n_]:=If[n===1, {{}}, Module[{cas}, Union[Sort/@Join@@(Tuples[rtall/@#]&/@IntegerPartitions[n-1])]]];
Table[Length[Select[rtall[n], Complement[Union@@#, #]==={}&]], {n, nn}]

Crossrefs

Cf. A000081, A004111, A279861, A290822.

Sequence in context: A206139 A023440 A225396 * A191869 A077373 A202278

Adjacent sequences: A290686 A290687 A290688 * A290690 A290691 A290692

Keyword

nonn,more

Author

Gus Wiseman, Oct 19 2017

Extensions

a(20) from Robert Price, Sep 13 2018

a(21)-a(22) from Robert P. P. McKone, Dec 16 2023

Status

approved