OFFSET
1,4
COMMENTS
We define an unlabeled ordered rooted tree to be transitive if every branch of a branch of the root already appears farther to the left as a branch of the root. An undirected version is A358454.
EXAMPLE
The a(1) = 1 through a(7) = 17 trees:
o (o) (oo) (ooo) (oooo) (ooooo) (oooooo)
(o(o)) (o(o)o) (o(o)oo) (o(o)ooo)
(o(oo)) (o(oo)o) (o(oo)oo)
(oo(o)) (o(ooo)) (o(ooo)o)
(oo(o)o) (o(oooo))
(oo(oo)) (oo(o)oo)
(ooo(o)) (oo(oo)o)
(o(o)(o)) (oo(ooo))
(ooo(o)o)
(ooo(oo))
(oooo(o))
(o(o)(o)o)
(o(o)(oo))
(o(o)o(o))
(o(oo)(o))
(oo(o)(o))
(o(o)((o)))
MATHEMATICA
aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n], Function[t, And@@Table[Complement[t[[k]], Take[t, k]]=={}, {k, Length[t]}]]]], {n, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 18 2022
STATUS
approved