OFFSET
1,1
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.
EXAMPLE
The terms together with their corresponding rooted trees begin:
2: (o)
6: (o(o))
7: ((oo))
9: ((o)(o))
20: (oo((o)))
22: (o(((o))))
23: (((o)(o)))
26: (o(o(o)))
27: ((o)(o)(o))
29: ((o((o))))
35: (((o))(oo))
41: (((o(o))))
66: (o(o)(((o))))
76: (oo(ooo))
78: (o(o)(o(o)))
79: ((o(((o)))))
84: (oo(o)(oo))
86: (o(o(oo)))
MATHEMATICA
stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
srt[n_]:=If[n==1, {}, srt/@stc[n-1]];
Select[Range[100], Count[srt[#], {}, {0, Infinity}]==Count[srt[#], _[__], {0, Infinity}]&]
CROSSREFS
These ordered trees are counted by A000891.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 25 2022
STATUS
approved