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A179752
Maximum depth of parenthesizations encoded by A014486, or correspondingly, maximum height for the equivalent general trees.
6
0, 1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4
OFFSET
0,4
COMMENTS
Each integer n appears first at position given by A014138.
LINKS
EXAMPLE
The terms A014486[1..8] encode the following rooted plane general trees:
.1.......2.......3.......4.......5.......6.......7.......8.
...........................................................
.........................................................o.
.........................................................|.
.................o.................o...o.......o...o.....o.
.................|.................|...|........\./......|.
.o.....o...o.....o.....o.o.o...o...o...o...o.....o.......o.
.|......\./......|......\|/.....\./.....\./......|.......|.
.*.......*.......*.......*.......*.......*.......*.......*.
and the corresponding parenthesizations:
.().....()()....(())...()()()..()(())..(())()..(()())..((()))
thus a(1)=1, a(2)=1, a(3)=2, a(4)=1, a(5)=2, a(6)=2, a(7)=2, a(8)=3.
MATHEMATICA
blist[m_] := Select[Map[Accumulate, Permutations[PadLeft[Table[1, m], 2*m, -1]]], Min[#] >= 0 &]; Join[{{0}}, Array[Map[Max, blist[#]] &, 6]] (* Paolo Xausa, Mar 04 2024 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Aug 03 2010
STATUS
approved