OFFSET
1,2
COMMENTS
We define the n-th standard ordered rooted tree to be obtained by taking the (n-1)-th composition in standard order (graded reverse-lexicographic, A066099) as root and replacing each part with its own standard ordered rooted tree. This ranking is an ordered variation of Matula-Goebel numbers, giving a bijective correspondence between positive integers and unlabeled ordered rooted trees.
LINKS
EXAMPLE
The initial terms and their corresponding trees:
1: o
4: (oo)
18: ((oo)o)
25: (o(oo))
137: ((oo)(oo))
262146: (((oo)o)o)
393217: (o((oo)o))
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
srt[n_]:=If[n==1, {}, srt/@stc[n-1]];
Select[Range[1000], FreeQ[srt[#], _[__]?(Length[#]!=2&)]&]
CROSSREFS
These trees are counted by A126120.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 14 2022
STATUS
approved