Processing math: 100%

Identifier
Values
[[],[]] => [[.,.],.] => 0
[[[]]] => [.,[.,.]] => 1
[[],[],[]] => [[[.,.],.],.] => 0
[[],[[]]] => [[.,.],[.,.]] => 1
[[[]],[]] => [[.,[.,.]],.] => 1
[[[],[]]] => [.,[[.,.],.]] => 1
[[[[]]]] => [.,[.,[.,.]]] => 2
[[],[],[],[]] => [[[[.,.],.],.],.] => 0
[[],[],[[]]] => [[[.,.],.],[.,.]] => 1
[[],[[]],[]] => [[[.,.],[.,.]],.] => 1
[[],[[],[]]] => [[.,.],[[.,.],.]] => 1
[[],[[[]]]] => [[.,.],[.,[.,.]]] => 2
[[[]],[],[]] => [[[.,[.,.]],.],.] => 1
[[[]],[[]]] => [[.,[.,.]],[.,.]] => 2
[[[],[]],[]] => [[.,[[.,.],.]],.] => 1
[[[[]]],[]] => [[.,[.,[.,.]]],.] => 2
[[[],[],[]]] => [.,[[[.,.],.],.]] => 1
[[[],[[]]]] => [.,[[.,.],[.,.]]] => 2
[[[[]],[]]] => [.,[[.,[.,.]],.]] => 2
[[[[],[]]]] => [.,[.,[[.,.],.]]] => 2
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => 3
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => 0
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => 1
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => 1
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => 1
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => 2
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => 1
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => 2
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => 1
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => 2
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => 1
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => 2
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => 2
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => 2
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => 3
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => 1
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => 2
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => 2
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => 2
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => 3
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => 1
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => 2
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => 2
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => 3
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => 1
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => 2
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => 2
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => 2
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => 3
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => 1
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => 2
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => 2
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => 2
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => 3
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => 2
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => 3
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => 2
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => 3
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => 2
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => 3
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => 3
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => 3
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => 4
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => 0
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => 1
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => 1
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => 1
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => 1
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => 2
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => 1
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => 2
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => 1
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => 2
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => 1
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => 2
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => 2
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => 2
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => 1
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => 2
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => 2
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => 1
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => 2
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => 2
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => 2
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => 1
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => 2
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => 2
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => 3
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => 2
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => 3
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => 2
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => 2
>>> Load all 195 entries. <<<
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => 3
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => 3
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => 3
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => 4
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => 1
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => 2
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => 2
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => 2
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => 3
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => 2
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => 2
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => 2
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => 3
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => 3
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => 3
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => 4
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => 1
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => 2
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => 2
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => 2
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => 2
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => 4
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => 1
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => 2
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => 2
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => 2
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => 3
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => 2
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => 3
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => 3
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => 1
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => 2
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => 2
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => 2
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => 3
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => 2
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => 3
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => 2
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => 3
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => 2
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => 3
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => 3
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => 3
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => 4
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => 1
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => 2
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => 2
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => 3
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => 2
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => 2
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => 3
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => 2
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => 2
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => 3
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => 3
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => 2
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => 3
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => 3
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => 2
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => 3
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => 3
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => 3
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => 4
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => 2
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => 3
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => 3
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => 3
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => 3
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => 4
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => 3
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size n−1 (where n is the size of t, and where t is an ordered tree) by the following recursive rule:
- if x is the left brother of y in t, then x becomes the left child of y;
- if x is the last child of y in t, then x becomes the right child of y,
and removing the root of t.