edit this statistic or download as text // json
Identifier
Values
[.,[.,.]] => 1
[[.,.],.] => 0
[.,[.,[.,.]]] => 2
[.,[[.,.],.]] => 1
[[.,.],[.,.]] => 1
[[.,[.,.]],.] => 1
[[[.,.],.],.] => 0
[.,[.,[.,[.,.]]]] => 3
[.,[.,[[.,.],.]]] => 2
[.,[[.,.],[.,.]]] => 2
[.,[[.,[.,.]],.]] => 2
[.,[[[.,.],.],.]] => 1
[[.,.],[.,[.,.]]] => 2
[[.,.],[[.,.],.]] => 1
[[.,[.,.]],[.,.]] => 2
[[[.,.],.],[.,.]] => 1
[[.,[.,[.,.]]],.] => 2
[[.,[[.,.],.]],.] => 1
[[[.,.],[.,.]],.] => 1
[[[.,[.,.]],.],.] => 1
[[[[.,.],.],.],.] => 0
[.,[.,[.,[.,[.,.]]]]] => 4
[.,[.,[.,[[.,.],.]]]] => 3
[.,[.,[[.,.],[.,.]]]] => 3
[.,[.,[[.,[.,.]],.]]] => 3
[.,[.,[[[.,.],.],.]]] => 2
[.,[[.,.],[.,[.,.]]]] => 3
[.,[[.,.],[[.,.],.]]] => 2
[.,[[.,[.,.]],[.,.]]] => 3
[.,[[[.,.],.],[.,.]]] => 2
[.,[[.,[.,[.,.]]],.]] => 3
[.,[[.,[[.,.],.]],.]] => 2
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 2
[.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[.,[.,.]]]] => 3
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 2
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 1
[[.,[.,.]],[.,[.,.]]] => 3
[[.,[.,.]],[[.,.],.]] => 2
[[[.,.],.],[.,[.,.]]] => 2
[[[.,.],.],[[.,.],.]] => 1
[[.,[.,[.,.]]],[.,.]] => 3
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 2
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 1
[[.,[.,[.,[.,.]]]],.] => 3
[[.,[.,[[.,.],.]]],.] => 2
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 2
[[.,[[[.,.],.],.]],.] => 1
[[[.,.],[.,[.,.]]],.] => 2
[[[.,.],[[.,.],.]],.] => 1
[[[.,[.,.]],[.,.]],.] => 2
[[[[.,.],.],[.,.]],.] => 1
[[[.,[.,[.,.]]],.],.] => 2
[[[.,[[.,.],.]],.],.] => 1
[[[[.,.],[.,.]],.],.] => 1
[[[[.,[.,.]],.],.],.] => 1
[[[[[.,.],.],.],.],.] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => 5
[.,[.,[.,[.,[[.,.],.]]]]] => 4
[.,[.,[.,[[.,.],[.,.]]]]] => 4
[.,[.,[.,[[.,[.,.]],.]]]] => 4
[.,[.,[.,[[[.,.],.],.]]]] => 3
[.,[.,[[.,.],[.,[.,.]]]]] => 4
[.,[.,[[.,.],[[.,.],.]]]] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => 4
[.,[.,[[[.,.],.],[.,.]]]] => 3
[.,[.,[[.,[.,[.,.]]],.]]] => 4
[.,[.,[[.,[[.,.],.]],.]]] => 3
[.,[.,[[[.,.],[.,.]],.]]] => 3
[.,[.,[[[.,[.,.]],.],.]]] => 3
[.,[.,[[[[.,.],.],.],.]]] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => 4
[.,[[.,.],[.,[[.,.],.]]]] => 3
[.,[[.,.],[[.,.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,.]],.]]] => 3
[.,[[.,.],[[[.,.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => 4
[.,[[.,[.,.]],[[.,.],.]]] => 3
[.,[[[.,.],.],[.,[.,.]]]] => 3
[.,[[[.,.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => 4
[.,[[.,[[.,.],.]],[.,.]]] => 3
[.,[[[.,.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,.]],.],[.,.]]] => 3
[.,[[[[.,.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => 4
[.,[[.,[.,[[.,.],.]]],.]] => 3
[.,[[.,[[.,.],[.,.]]],.]] => 3
[.,[[.,[[.,[.,.]],.]],.]] => 3
[.,[[.,[[[.,.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => 3
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 3
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 3
>>> Load all 195 entries. <<<
[.,[[[.,[[.,.],.]],.],.]] => 2
[.,[[[[.,.],[.,.]],.],.]] => 2
[.,[[[[.,[.,.]],.],.],.]] => 2
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 4
[[.,.],[.,[.,[[.,.],.]]]] => 3
[[.,.],[.,[[.,.],[.,.]]]] => 3
[[.,.],[.,[[.,[.,.]],.]]] => 3
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 3
[[.,.],[[.,.],[[.,.],.]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => 3
[[.,.],[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => 3
[[.,.],[[.,[[.,.],.]],.]] => 2
[[.,.],[[[.,.],[.,.]],.]] => 2
[[.,.],[[[.,[.,.]],.],.]] => 2
[[.,.],[[[[.,.],.],.],.]] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => 4
[[.,[.,.]],[.,[[.,.],.]]] => 3
[[.,[.,.]],[[.,.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,.]],.]] => 3
[[.,[.,.]],[[[.,.],.],.]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => 3
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => 4
[[.,[.,[.,.]]],[[.,.],.]] => 3
[[.,[[.,.],.]],[.,[.,.]]] => 3
[[.,[[.,.],.]],[[.,.],.]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => 3
[[[.,.],[.,.]],[[.,.],.]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => 3
[[[.,[.,.]],.],[[.,.],.]] => 2
[[[[.,.],.],.],[.,[.,.]]] => 2
[[[[.,.],.],.],[[.,.],.]] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => 4
[[.,[.,[[.,.],.]]],[.,.]] => 3
[[.,[[.,.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,.]],.]],[.,.]] => 3
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 3
[[[.,.],[[.,.],.]],[.,.]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[.,.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => 3
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 2
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => 4
[[.,[.,[.,[[.,.],.]]]],.] => 3
[[.,[.,[[.,.],[.,.]]]],.] => 3
[[.,[.,[[.,[.,.]],.]]],.] => 3
[[.,[.,[[[.,.],.],.]]],.] => 2
[[.,[[.,.],[.,[.,.]]]],.] => 3
[[.,[[.,.],[[.,.],.]]],.] => 2
[[.,[[.,[.,.]],[.,.]]],.] => 3
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 3
[[.,[[.,[[.,.],.]],.]],.] => 2
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 2
[[.,[[[[.,.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,.]]]],.] => 3
[[[.,.],[.,[[.,.],.]]],.] => 2
[[[.,.],[[.,.],[.,.]]],.] => 2
[[[.,.],[[.,[.,.]],.]],.] => 2
[[[.,.],[[[.,.],.],.]],.] => 1
[[[.,[.,.]],[.,[.,.]]],.] => 3
[[[.,[.,.]],[[.,.],.]],.] => 2
[[[[.,.],.],[.,[.,.]]],.] => 2
[[[[.,.],.],[[.,.],.]],.] => 1
[[[.,[.,[.,.]]],[.,.]],.] => 3
[[[.,[[.,.],.]],[.,.]],.] => 2
[[[[.,.],[.,.]],[.,.]],.] => 2
[[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[.,.],.],.],[.,.]],.] => 1
[[[.,[.,[.,[.,.]]]],.],.] => 3
[[[.,[.,[[.,.],.]]],.],.] => 2
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 2
[[[.,[[[.,.],.],.]],.],.] => 1
[[[[.,.],[.,[.,.]]],.],.] => 2
[[[[.,.],[[.,.],.]],.],.] => 1
[[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[.,.],.],[.,.]],.],.] => 1
[[[[.,[.,[.,.]]],.],.],.] => 2
[[[[.,[[.,.],.]],.],.],.] => 1
[[[[[.,.],[.,.]],.],.],.] => 1
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 0
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Description
The number of left oriented leafs of a binary tree except the first one.
In other other words, this is the sum of canopee vector of the tree.
The canopee of a non empty binary tree T with n internal nodes is the list l of 0 and 1 of length n-1 obtained by going along the leaves of T from left to right except the two extremal ones, writing 0 if the leaf is a right leaf and 1 if the leaf is a left leaf.
This is also the number of nodes having a right child. Indeed each of said right children will give exactly one left oriented leaf.
Code
def statistic(bt):
    return sum(bt.canopee())
Created
Jun 13, 2013 at 10:02 by Viviane Pons
Updated
Oct 17, 2015 at 10:48 by Christian Stump