Identifier
Values
[.,.] => [[]] => 1
[.,[.,.]] => [[[]]] => 1
[[.,.],.] => [[],[]] => 2
[.,[.,[.,.]]] => [[[[]]]] => 1
[.,[[.,.],.]] => [[[],[]]] => 1
[[.,.],[.,.]] => [[],[[]]] => 2
[[.,[.,.]],.] => [[[]],[]] => 2
[[[.,.],.],.] => [[],[],[]] => 3
[.,[.,[.,[.,.]]]] => [[[[[]]]]] => 1
[.,[.,[[.,.],.]]] => [[[[],[]]]] => 1
[.,[[.,.],[.,.]]] => [[[],[[]]]] => 1
[.,[[.,[.,.]],.]] => [[[[]],[]]] => 1
[.,[[[.,.],.],.]] => [[[],[],[]]] => 1
[[.,.],[.,[.,.]]] => [[],[[[]]]] => 2
[[.,.],[[.,.],.]] => [[],[[],[]]] => 2
[[.,[.,.]],[.,.]] => [[[]],[[]]] => 2
[[[.,.],.],[.,.]] => [[],[],[[]]] => 3
[[.,[.,[.,.]]],.] => [[[[]]],[]] => 2
[[.,[[.,.],.]],.] => [[[],[]],[]] => 2
[[[.,.],[.,.]],.] => [[],[[]],[]] => 3
[[[.,[.,.]],.],.] => [[[]],[],[]] => 3
[[[[.,.],.],.],.] => [[],[],[],[]] => 4
[.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => 1
[.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => 1
[.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => 1
[.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]] => 1
[.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => 1
[.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 1
[.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 1
[.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 1
[.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 1
[.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => 1
[.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => 1
[.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => 1
[.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => 1
[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => 1
[[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 2
[[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 2
[[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 2
[[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 2
[[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 2
[[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 2
[[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 2
[[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 3
[[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 3
[[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 2
[[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 2
[[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 3
[[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 3
[[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 4
[[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => 2
[[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => 2
[[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => 2
[[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]] => 2
[[.,[[[.,.],.],.]],.] => [[[],[],[]],[]] => 2
[[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 3
[[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 3
[[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 3
[[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 4
[[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => 3
[[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => 3
[[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 4
[[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => 4
[[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => 5
[.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [[[[[[]],[]]]]] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 1
[.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [[[[[[]]],[]]]] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [[[[[],[]],[]]]] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [[[[[]],[],[]]]] => 1
[.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 1
[.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 1
[.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 1
[.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 1
[.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 1
[.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 1
[.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [[[[[]],[]],[]]] => 1
[.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 1
[.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 1
[.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 1
[.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 1
>>> Load all 196 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [[[[[]]],[],[]]] => 1
[.,[[[.,[[.,.],.]],.],.]] => [[[[],[]],[],[]]] => 1
[.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => 1
[.,[[[[.,[.,.]],.],.],.]] => [[[[]],[],[],[]]] => 1
[.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 2
[[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 2
[[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 2
[[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 2
[[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 2
[[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 2
[[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 3
[[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 3
[[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 3
[[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 3
[[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 3
[[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 3
[[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 3
[[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 4
[[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 4
[[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 2
[[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 3
[[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 4
[[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 3
[[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 3
[[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 4
[[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 4
[[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 5
[[.,[.,[.,[.,[.,.]]]]],.] => [[[[[[]]]]],[]] => 2
[[.,[.,[.,[[.,.],.]]]],.] => [[[[[],[]]]],[]] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [[[[],[[]]]],[]] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [[[[[]],[]]],[]] => 2
[[.,[.,[[[.,.],.],.]]],.] => [[[[],[],[]]],[]] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 2
[[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 2
[[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [[[[[]]],[]],[]] => 2
[[.,[[.,[[.,.],.]],.]],.] => [[[[],[]],[]],[]] => 2
[[.,[[[.,.],[.,.]],.]],.] => [[[],[[]],[]],[]] => 2
[[.,[[[.,[.,.]],.],.]],.] => [[[[]],[],[]],[]] => 2
[[.,[[[[.,.],.],.],.]],.] => [[[],[],[],[]],[]] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 3
[[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 3
[[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 3
[[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 3
[[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 3
[[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 3
[[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 4
[[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 4
[[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 3
[[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 3
[[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 4
[[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 4
[[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 5
[[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => 3
[[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => 3
[[[.,[[.,.],[.,.]]],.],.] => [[[],[[]]],[],[]] => 3
[[[.,[[.,[.,.]],.]],.],.] => [[[[]],[]],[],[]] => 3
[[[.,[[[.,.],.],.]],.],.] => [[[],[],[]],[],[]] => 3
[[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 4
[[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 4
[[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 4
[[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 5
[[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => 4
[[[[.,[[.,.],.]],.],.],.] => [[[],[]],[],[],[]] => 4
[[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 5
[[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => 5
[[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => 6
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Description
The number of subtrees.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.