A179752 Maximum depth of parenthesizations encoded by A014486, or correspondingly, maximum height for the equivalent general trees.

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

Author

Antti Karttunen, Aug 03 2010

Keywords

• nonn
• base

Comments

Each integer n appears first at position given by A014138.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2055

Crossrefs

Cf. A179751, A126303, A126304, A080237, A085197.

Programs

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 *)