A290689 - OEIS

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

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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.

Regarding the notation, a rooted tree is a finite multiset of rooted trees. For example, the rooted tree (o(o)(oo)) is short for {{},{{}},{{},{}}}. Each "o" is a leaf. Each pair of parentheses corresponds to a non-leaf node (such as the root). Its contents "(...)" represent a branch. - Gus Wiseman, Nov 16 2024

LINKS

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

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

EXAMPLE

The a(7) = 8 7-node transitive rooted 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

The restriction to identity trees (A004111) is A279861, ranks A290760.

These trees are ranked by A290822.