Identifier
Identifier
Values
[.,[.,.]] generating graphics... => 1
[[.,.],.] generating graphics... => 2
[.,[.,[.,.]]] generating graphics... => 1
[.,[[.,.],.]] generating graphics... => 1
[[.,.],[.,.]] generating graphics... => 2
[[.,[.,.]],.] generating graphics... => 2
[[[.,.],.],.] generating graphics... => 3
[.,[.,[.,[.,.]]]] generating graphics... => 1
[.,[.,[[.,.],.]]] generating graphics... => 1
[.,[[.,.],[.,.]]] generating graphics... => 1
[.,[[.,[.,.]],.]] generating graphics... => 1
[.,[[[.,.],.],.]] generating graphics... => 1
[[.,.],[.,[.,.]]] generating graphics... => 2
[[.,.],[[.,.],.]] generating graphics... => 2
[[.,[.,.]],[.,.]] generating graphics... => 2
[[[.,.],.],[.,.]] generating graphics... => 3
[[.,[.,[.,.]]],.] generating graphics... => 2
[[.,[[.,.],.]],.] generating graphics... => 2
[[[.,.],[.,.]],.] generating graphics... => 3
[[[.,[.,.]],.],.] generating graphics... => 3
[[[[.,.],.],.],.] generating graphics... => 4
[.,[.,[.,[.,[.,.]]]]] generating graphics... => 1
[.,[.,[.,[[.,.],.]]]] generating graphics... => 1
[.,[.,[[.,.],[.,.]]]] generating graphics... => 1
[.,[.,[[.,[.,.]],.]]] generating graphics... => 1
[.,[.,[[[.,.],.],.]]] generating graphics... => 1
[.,[[.,.],[.,[.,.]]]] generating graphics... => 1
[.,[[.,.],[[.,.],.]]] generating graphics... => 1
[.,[[.,[.,.]],[.,.]]] generating graphics... => 1
[.,[[[.,.],.],[.,.]]] generating graphics... => 1
[.,[[.,[.,[.,.]]],.]] generating graphics... => 1
[.,[[.,[[.,.],.]],.]] generating graphics... => 1
[.,[[[.,.],[.,.]],.]] generating graphics... => 1
[.,[[[.,[.,.]],.],.]] generating graphics... => 1
[.,[[[[.,.],.],.],.]] generating graphics... => 1
[[.,.],[.,[.,[.,.]]]] generating graphics... => 2
[[.,.],[.,[[.,.],.]]] generating graphics... => 2
[[.,.],[[.,.],[.,.]]] generating graphics... => 2
[[.,.],[[.,[.,.]],.]] generating graphics... => 2
[[.,.],[[[.,.],.],.]] generating graphics... => 2
[[.,[.,.]],[.,[.,.]]] generating graphics... => 2
[[.,[.,.]],[[.,.],.]] generating graphics... => 2
[[[.,.],.],[.,[.,.]]] generating graphics... => 3
[[[.,.],.],[[.,.],.]] generating graphics... => 3
[[.,[.,[.,.]]],[.,.]] generating graphics... => 2
[[.,[[.,.],.]],[.,.]] generating graphics... => 2
[[[.,.],[.,.]],[.,.]] generating graphics... => 3
[[[.,[.,.]],.],[.,.]] generating graphics... => 3
[[[[.,.],.],.],[.,.]] generating graphics... => 4
[[.,[.,[.,[.,.]]]],.] generating graphics... => 2
[[.,[.,[[.,.],.]]],.] generating graphics... => 2
[[.,[[.,.],[.,.]]],.] generating graphics... => 2
[[.,[[.,[.,.]],.]],.] generating graphics... => 2
[[.,[[[.,.],.],.]],.] generating graphics... => 2
[[[.,.],[.,[.,.]]],.] generating graphics... => 3
[[[.,.],[[.,.],.]],.] generating graphics... => 3
[[[.,[.,.]],[.,.]],.] generating graphics... => 3
[[[[.,.],.],[.,.]],.] generating graphics... => 4
[[[.,[.,[.,.]]],.],.] generating graphics... => 3
[[[.,[[.,.],.]],.],.] generating graphics... => 3
[[[[.,.],[.,.]],.],.] generating graphics... => 4
[[[[.,[.,.]],.],.],.] generating graphics... => 4
[[[[[.,.],.],.],.],.] generating graphics... => 5
[.,[.,[.,[.,[.,[.,.]]]]]] generating graphics... => 1
[.,[.,[.,[.,[[.,.],.]]]]] generating graphics... => 1
[.,[.,[.,[[.,.],[.,.]]]]] generating graphics... => 1
[.,[.,[.,[[.,[.,.]],.]]]] generating graphics... => 1
[.,[.,[.,[[[.,.],.],.]]]] generating graphics... => 1
[.,[.,[[.,.],[.,[.,.]]]]] generating graphics... => 1
[.,[.,[[.,.],[[.,.],.]]]] generating graphics... => 1
[.,[.,[[.,[.,.]],[.,.]]]] generating graphics... => 1
[.,[.,[[[.,.],.],[.,.]]]] generating graphics... => 1
[.,[.,[[.,[.,[.,.]]],.]]] generating graphics... => 1
[.,[.,[[.,[[.,.],.]],.]]] generating graphics... => 1
[.,[.,[[[.,.],[.,.]],.]]] generating graphics... => 1
[.,[.,[[[.,[.,.]],.],.]]] generating graphics... => 1
[.,[.,[[[[.,.],.],.],.]]] generating graphics... => 1
[.,[[.,.],[.,[.,[.,.]]]]] generating graphics... => 1
[.,[[.,.],[.,[[.,.],.]]]] generating graphics... => 1
[.,[[.,.],[[.,.],[.,.]]]] generating graphics... => 1
[.,[[.,.],[[.,[.,.]],.]]] generating graphics... => 1
[.,[[.,.],[[[.,.],.],.]]] generating graphics... => 1
[.,[[.,[.,.]],[.,[.,.]]]] generating graphics... => 1
[.,[[.,[.,.]],[[.,.],.]]] generating graphics... => 1
[.,[[[.,.],.],[.,[.,.]]]] generating graphics... => 1
[.,[[[.,.],.],[[.,.],.]]] generating graphics... => 1
[.,[[.,[.,[.,.]]],[.,.]]] generating graphics... => 1
[.,[[.,[[.,.],.]],[.,.]]] generating graphics... => 1
[.,[[[.,.],[.,.]],[.,.]]] generating graphics... => 1
[.,[[[.,[.,.]],.],[.,.]]] generating graphics... => 1
[.,[[[[.,.],.],.],[.,.]]] generating graphics... => 1
[.,[[.,[.,[.,[.,.]]]],.]] generating graphics... => 1
[.,[[.,[.,[[.,.],.]]],.]] generating graphics... => 1
[.,[[.,[[.,.],[.,.]]],.]] generating graphics... => 1
[.,[[.,[[.,[.,.]],.]],.]] generating graphics... => 1
[.,[[.,[[[.,.],.],.]],.]] generating graphics... => 1
[.,[[[.,.],[.,[.,.]]],.]] generating graphics... => 1
[.,[[[.,.],[[.,.],.]],.]] generating graphics... => 1
[.,[[[.,[.,.]],[.,.]],.]] generating graphics... => 1
[.,[[[[.,.],.],[.,.]],.]] generating graphics... => 1
[.,[[[.,[.,[.,.]]],.],.]] generating graphics... => 1
[.,[[[.,[[.,.],.]],.],.]] generating graphics... => 1
[.,[[[[.,.],[.,.]],.],.]] generating graphics... => 1
[.,[[[[.,[.,.]],.],.],.]] generating graphics... => 1
[.,[[[[[.,.],.],.],.],.]] generating graphics... => 1
[[.,.],[.,[.,[.,[.,.]]]]] generating graphics... => 2
[[.,.],[.,[.,[[.,.],.]]]] generating graphics... => 2
[[.,.],[.,[[.,.],[.,.]]]] generating graphics... => 2
[[.,.],[.,[[.,[.,.]],.]]] generating graphics... => 2
[[.,.],[.,[[[.,.],.],.]]] generating graphics... => 2
[[.,.],[[.,.],[.,[.,.]]]] generating graphics... => 2
[[.,.],[[.,.],[[.,.],.]]] generating graphics... => 2
[[.,.],[[.,[.,.]],[.,.]]] generating graphics... => 2
[[.,.],[[[.,.],.],[.,.]]] generating graphics... => 2
[[.,.],[[.,[.,[.,.]]],.]] generating graphics... => 2
[[.,.],[[.,[[.,.],.]],.]] generating graphics... => 2
[[.,.],[[[.,.],[.,.]],.]] generating graphics... => 2
[[.,.],[[[.,[.,.]],.],.]] generating graphics... => 2
[[.,.],[[[[.,.],.],.],.]] generating graphics... => 2
[[.,[.,.]],[.,[.,[.,.]]]] generating graphics... => 2
[[.,[.,.]],[.,[[.,.],.]]] generating graphics... => 2
[[.,[.,.]],[[.,.],[.,.]]] generating graphics... => 2
[[.,[.,.]],[[.,[.,.]],.]] generating graphics... => 2
[[.,[.,.]],[[[.,.],.],.]] generating graphics... => 2
[[[.,.],.],[.,[.,[.,.]]]] generating graphics... => 3
[[[.,.],.],[.,[[.,.],.]]] generating graphics... => 3
[[[.,.],.],[[.,.],[.,.]]] generating graphics... => 3
[[[.,.],.],[[.,[.,.]],.]] generating graphics... => 3
[[[.,.],.],[[[.,.],.],.]] generating graphics... => 3
[[.,[.,[.,.]]],[.,[.,.]]] generating graphics... => 2
[[.,[.,[.,.]]],[[.,.],.]] generating graphics... => 2
[[.,[[.,.],.]],[.,[.,.]]] generating graphics... => 2
[[.,[[.,.],.]],[[.,.],.]] generating graphics... => 2
[[[.,.],[.,.]],[.,[.,.]]] generating graphics... => 3
[[[.,.],[.,.]],[[.,.],.]] generating graphics... => 3
[[[.,[.,.]],.],[.,[.,.]]] generating graphics... => 3
[[[.,[.,.]],.],[[.,.],.]] generating graphics... => 3
[[[[.,.],.],.],[.,[.,.]]] generating graphics... => 4
[[[[.,.],.],.],[[.,.],.]] generating graphics... => 4
[[.,[.,[.,[.,.]]]],[.,.]] generating graphics... => 2
[[.,[.,[[.,.],.]]],[.,.]] generating graphics... => 2
[[.,[[.,.],[.,.]]],[.,.]] generating graphics... => 2
[[.,[[.,[.,.]],.]],[.,.]] generating graphics... => 2
[[.,[[[.,.],.],.]],[.,.]] generating graphics... => 2
[[[.,.],[.,[.,.]]],[.,.]] generating graphics... => 3
[[[.,.],[[.,.],.]],[.,.]] generating graphics... => 3
[[[.,[.,.]],[.,.]],[.,.]] generating graphics... => 3
[[[[.,.],.],[.,.]],[.,.]] generating graphics... => 4
[[[.,[.,[.,.]]],.],[.,.]] generating graphics... => 3
[[[.,[[.,.],.]],.],[.,.]] generating graphics... => 3
[[[[.,.],[.,.]],.],[.,.]] generating graphics... => 4
[[[[.,[.,.]],.],.],[.,.]] generating graphics... => 4
[[[[[.,.],.],.],.],[.,.]] generating graphics... => 5
[[.,[.,[.,[.,[.,.]]]]],.] generating graphics... => 2
[[.,[.,[.,[[.,.],.]]]],.] generating graphics... => 2
[[.,[.,[[.,.],[.,.]]]],.] generating graphics... => 2
[[.,[.,[[.,[.,.]],.]]],.] generating graphics... => 2
[[.,[.,[[[.,.],.],.]]],.] generating graphics... => 2
[[.,[[.,.],[.,[.,.]]]],.] generating graphics... => 2
[[.,[[.,.],[[.,.],.]]],.] generating graphics... => 2
[[.,[[.,[.,.]],[.,.]]],.] generating graphics... => 2
[[.,[[[.,.],.],[.,.]]],.] generating graphics... => 2
[[.,[[.,[.,[.,.]]],.]],.] generating graphics... => 2
[[.,[[.,[[.,.],.]],.]],.] generating graphics... => 2
[[.,[[[.,.],[.,.]],.]],.] generating graphics... => 2
[[.,[[[.,[.,.]],.],.]],.] generating graphics... => 2
[[.,[[[[.,.],.],.],.]],.] generating graphics... => 2
[[[.,.],[.,[.,[.,.]]]],.] generating graphics... => 3
[[[.,.],[.,[[.,.],.]]],.] generating graphics... => 3
[[[.,.],[[.,.],[.,.]]],.] generating graphics... => 3
[[[.,.],[[.,[.,.]],.]],.] generating graphics... => 3
[[[.,.],[[[.,.],.],.]],.] generating graphics... => 3
[[[.,[.,.]],[.,[.,.]]],.] generating graphics... => 3
[[[.,[.,.]],[[.,.],.]],.] generating graphics... => 3
[[[[.,.],.],[.,[.,.]]],.] generating graphics... => 4
[[[[.,.],.],[[.,.],.]],.] generating graphics... => 4
[[[.,[.,[.,.]]],[.,.]],.] generating graphics... => 3
[[[.,[[.,.],.]],[.,.]],.] generating graphics... => 3
[[[[.,.],[.,.]],[.,.]],.] generating graphics... => 4
[[[[.,[.,.]],.],[.,.]],.] generating graphics... => 4
[[[[[.,.],.],.],[.,.]],.] generating graphics... => 5
[[[.,[.,[.,[.,.]]]],.],.] generating graphics... => 3
[[[.,[.,[[.,.],.]]],.],.] generating graphics... => 3
[[[.,[[.,.],[.,.]]],.],.] generating graphics... => 3
[[[.,[[.,[.,.]],.]],.],.] generating graphics... => 3
[[[.,[[[.,.],.],.]],.],.] generating graphics... => 3
[[[[.,.],[.,[.,.]]],.],.] generating graphics... => 4
[[[[.,.],[[.,.],.]],.],.] generating graphics... => 4
[[[[.,[.,.]],[.,.]],.],.] generating graphics... => 4
[[[[[.,.],.],[.,.]],.],.] generating graphics... => 5
[[[[.,[.,[.,.]]],.],.],.] generating graphics... => 4
[[[[.,[[.,.],.]],.],.],.] generating graphics... => 4
[[[[[.,.],[.,.]],.],.],.] generating graphics... => 5
[[[[[.,[.,.]],.],.],.],.] generating graphics... => 5
[[[[[[.,.],.],.],.],.],.] generating graphics... => 6
click to show generating function       
Description
The number of nodes on the left branch of a binary tree.
Also corresponds to ST000011 after applying the Tamari bijection between binary trees and Dyck path.
References
[1] Chapoton, F. Sur le nombre d'intervalles dans les treillis de Tamari MathSciNet:2264942
Code
def statistic(tree):
    if(not tree):
        return 0
    else: return 1 + statistic(tree[0])
Created
Apr 30, 2013 at 11:04 by Viviane Pons
Updated
Oct 17, 2015 at 10:47 by Christian Stump