Identifier
-
Mp00010:
Binary trees
—to ordered tree: left child = left brother⟶
Ordered trees
St000975: Ordered trees ⟶ ℤ
Values
[.,.] => [[]] => 1
[.,[.,.]] => [[[]]] => 2
[[.,.],.] => [[],[]] => 2
[.,[.,[.,.]]] => [[[[]]]] => 3
[.,[[.,.],.]] => [[[],[]]] => 3
[[.,.],[.,.]] => [[],[[]]] => 3
[[.,[.,.]],.] => [[[]],[]] => 3
[[[.,.],.],.] => [[],[],[]] => 2
[.,[.,[.,[.,.]]]] => [[[[[]]]]] => 4
[.,[.,[[.,.],.]]] => [[[[],[]]]] => 4
[.,[[.,.],[.,.]]] => [[[],[[]]]] => 4
[.,[[.,[.,.]],.]] => [[[[]],[]]] => 4
[.,[[[.,.],.],.]] => [[[],[],[]]] => 3
[[.,.],[.,[.,.]]] => [[],[[[]]]] => 4
[[.,.],[[.,.],.]] => [[],[[],[]]] => 3
[[.,[.,.]],[.,.]] => [[[]],[[]]] => 4
[[[.,.],.],[.,.]] => [[],[],[[]]] => 3
[[.,[.,[.,.]]],.] => [[[[]]],[]] => 4
[[.,[[.,.],.]],.] => [[[],[]],[]] => 3
[[[.,.],[.,.]],.] => [[],[[]],[]] => 2
[[[.,[.,.]],.],.] => [[[]],[],[]] => 3
[[[[.,.],.],.],.] => [[],[],[],[]] => 2
[.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => 5
[.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => 5
[.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => 5
[.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]] => 5
[.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => 4
[.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => 5
[.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => 4
[.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => 5
[.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => 4
[.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => 5
[.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => 4
[.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => 3
[.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => 4
[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => 3
[[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => 5
[[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => 4
[[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => 4
[[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => 3
[[.,.],[[[.,.],.],.]] => [[],[[],[],[]]] => 3
[[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => 5
[[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => 4
[[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => 4
[[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => 3
[[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => 5
[[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => 4
[[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => 3
[[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => 4
[[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => 3
[[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => 5
[[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => 4
[[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => 3
[[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]] => 4
[[.,[[[.,.],.],.]],.] => [[[],[],[]],[]] => 3
[[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => 2
[[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => 2
[[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => 3
[[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => 2
[[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => 4
[[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => 3
[[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => 2
[[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => 3
[[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => 2
[.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]] => 6
[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]] => 6
[.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]] => 6
[.,[.,[.,[[.,[.,.]],.]]]] => [[[[[[]],[]]]]] => 6
[.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]] => 5
[.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]] => 6
[.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]] => 5
[.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]] => 6
[.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]] => 5
[.,[.,[[.,[.,[.,.]]],.]]] => [[[[[[]]],[]]]] => 6
[.,[.,[[.,[[.,.],.]],.]]] => [[[[[],[]],[]]]] => 5
[.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]] => 4
[.,[.,[[[.,[.,.]],.],.]]] => [[[[[]],[],[]]]] => 5
[.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]] => 4
[.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]] => 6
[.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]] => 5
[.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]] => 5
[.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]] => 4
[.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]] => 4
[.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]] => 6
[.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]] => 5
[.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]] => 5
[.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]] => 4
[.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]] => 6
[.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]] => 5
[.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]] => 4
[.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]] => 5
[.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]] => 4
[.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]] => 6
[.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]] => 5
[.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]] => 4
[.,[[.,[[.,[.,.]],.]],.]] => [[[[[]],[]],[]]] => 5
[.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]] => 4
[.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]] => 3
[.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]] => 3
[.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]] => 4
[.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]] => 3
>>> Load all 1200 entries. <<<[.,[[[.,[.,[.,.]]],.],.]] => [[[[[]]],[],[]]] => 5
[.,[[[.,[[.,.],.]],.],.]] => [[[[],[]],[],[]]] => 4
[.,[[[[.,.],[.,.]],.],.]] => [[[],[[]],[],[]]] => 3
[.,[[[[.,[.,.]],.],.],.]] => [[[[]],[],[],[]]] => 4
[.,[[[[[.,.],.],.],.],.]] => [[[],[],[],[],[]]] => 3
[[.,.],[.,[.,[.,[.,.]]]]] => [[],[[[[[]]]]]] => 6
[[.,.],[.,[.,[[.,.],.]]]] => [[],[[[[],[]]]]] => 5
[[.,.],[.,[[.,.],[.,.]]]] => [[],[[[],[[]]]]] => 5
[[.,.],[.,[[.,[.,.]],.]]] => [[],[[[[]],[]]]] => 4
[[.,.],[.,[[[.,.],.],.]]] => [[],[[[],[],[]]]] => 4
[[.,.],[[.,.],[.,[.,.]]]] => [[],[[],[[[]]]]] => 5
[[.,.],[[.,.],[[.,.],.]]] => [[],[[],[[],[]]]] => 4
[[.,.],[[.,[.,.]],[.,.]]] => [[],[[[]],[[]]]] => 4
[[.,.],[[[.,.],.],[.,.]]] => [[],[[],[],[[]]]] => 4
[[.,.],[[.,[.,[.,.]]],.]] => [[],[[[[]]],[]]] => 3
[[.,.],[[.,[[.,.],.]],.]] => [[],[[[],[]],[]]] => 3
[[.,.],[[[.,.],[.,.]],.]] => [[],[[],[[]],[]]] => 3
[[.,.],[[[.,[.,.]],.],.]] => [[],[[[]],[],[]]] => 3
[[.,.],[[[[.,.],.],.],.]] => [[],[[],[],[],[]]] => 3
[[.,[.,.]],[.,[.,[.,.]]]] => [[[]],[[[[]]]]] => 6
[[.,[.,.]],[.,[[.,.],.]]] => [[[]],[[[],[]]]] => 5
[[.,[.,.]],[[.,.],[.,.]]] => [[[]],[[],[[]]]] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [[[]],[[[]],[]]] => 4
[[.,[.,.]],[[[.,.],.],.]] => [[[]],[[],[],[]]] => 4
[[[.,.],.],[.,[.,[.,.]]]] => [[],[],[[[[]]]]] => 5
[[[.,.],.],[.,[[.,.],.]]] => [[],[],[[[],[]]]] => 4
[[[.,.],.],[[.,.],[.,.]]] => [[],[],[[],[[]]]] => 4
[[[.,.],.],[[.,[.,.]],.]] => [[],[],[[[]],[]]] => 3
[[[.,.],.],[[[.,.],.],.]] => [[],[],[[],[],[]]] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [[[[]]],[[[]]]] => 6
[[.,[.,[.,.]]],[[.,.],.]] => [[[[]]],[[],[]]] => 5
[[.,[[.,.],.]],[.,[.,.]]] => [[[],[]],[[[]]]] => 5
[[.,[[.,.],.]],[[.,.],.]] => [[[],[]],[[],[]]] => 4
[[[.,.],[.,.]],[.,[.,.]]] => [[],[[]],[[[]]]] => 4
[[[.,.],[.,.]],[[.,.],.]] => [[],[[]],[[],[]]] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [[[]],[],[[[]]]] => 5
[[[.,[.,.]],.],[[.,.],.]] => [[[]],[],[[],[]]] => 4
[[[[.,.],.],.],[.,[.,.]]] => [[],[],[],[[[]]]] => 4
[[[[.,.],.],.],[[.,.],.]] => [[],[],[],[[],[]]] => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [[[[[]]]],[[]]] => 6
[[.,[.,[[.,.],.]]],[.,.]] => [[[[],[]]],[[]]] => 5
[[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]]],[[]]] => 4
[[.,[[.,[.,.]],.]],[.,.]] => [[[[]],[]],[[]]] => 5
[[.,[[[.,.],.],.]],[.,.]] => [[[],[],[]],[[]]] => 4
[[[.,.],[.,[.,.]]],[.,.]] => [[],[[[]]],[[]]] => 3
[[[.,.],[[.,.],.]],[.,.]] => [[],[[],[]],[[]]] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [[[]],[[]],[[]]] => 4
[[[[.,.],.],[.,.]],[.,.]] => [[],[],[[]],[[]]] => 3
[[[.,[.,[.,.]]],.],[.,.]] => [[[[]]],[],[[]]] => 5
[[[.,[[.,.],.]],.],[.,.]] => [[[],[]],[],[[]]] => 4
[[[[.,.],[.,.]],.],[.,.]] => [[],[[]],[],[[]]] => 3
[[[[.,[.,.]],.],.],[.,.]] => [[[]],[],[],[[]]] => 4
[[[[[.,.],.],.],.],[.,.]] => [[],[],[],[],[[]]] => 3
[[.,[.,[.,[.,[.,.]]]]],.] => [[[[[[]]]]],[]] => 6
[[.,[.,[.,[[.,.],.]]]],.] => [[[[[],[]]]],[]] => 5
[[.,[.,[[.,.],[.,.]]]],.] => [[[[],[[]]]],[]] => 4
[[.,[.,[[.,[.,.]],.]]],.] => [[[[[]],[]]],[]] => 5
[[.,[.,[[[.,.],.],.]]],.] => [[[[],[],[]]],[]] => 4
[[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[]]]],[]] => 3
[[.,[[.,.],[[.,.],.]]],.] => [[[],[[],[]]],[]] => 3
[[.,[[.,[.,.]],[.,.]]],.] => [[[[]],[[]]],[]] => 4
[[.,[[[.,.],.],[.,.]]],.] => [[[],[],[[]]],[]] => 3
[[.,[[.,[.,[.,.]]],.]],.] => [[[[[]]],[]],[]] => 5
[[.,[[.,[[.,.],.]],.]],.] => [[[[],[]],[]],[]] => 4
[[.,[[[.,.],[.,.]],.]],.] => [[[],[[]],[]],[]] => 3
[[.,[[[.,[.,.]],.],.]],.] => [[[[]],[],[]],[]] => 4
[[.,[[[[.,.],.],.],.]],.] => [[[],[],[],[]],[]] => 3
[[[.,.],[.,[.,[.,.]]]],.] => [[],[[[[]]]],[]] => 2
[[[.,.],[.,[[.,.],.]]],.] => [[],[[[],[]]],[]] => 2
[[[.,.],[[.,.],[.,.]]],.] => [[],[[],[[]]],[]] => 2
[[[.,.],[[.,[.,.]],.]],.] => [[],[[[]],[]],[]] => 2
[[[.,.],[[[.,.],.],.]],.] => [[],[[],[],[]],[]] => 2
[[[.,[.,.]],[.,[.,.]]],.] => [[[]],[[[]]],[]] => 3
[[[.,[.,.]],[[.,.],.]],.] => [[[]],[[],[]],[]] => 3
[[[[.,.],.],[.,[.,.]]],.] => [[],[],[[[]]],[]] => 2
[[[[.,.],.],[[.,.],.]],.] => [[],[],[[],[]],[]] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [[[[]]],[[]],[]] => 4
[[[.,[[.,.],.]],[.,.]],.] => [[[],[]],[[]],[]] => 3
[[[[.,.],[.,.]],[.,.]],.] => [[],[[]],[[]],[]] => 2
[[[[.,[.,.]],.],[.,.]],.] => [[[]],[],[[]],[]] => 3
[[[[[.,.],.],.],[.,.]],.] => [[],[],[],[[]],[]] => 2
[[[.,[.,[.,[.,.]]]],.],.] => [[[[[]]]],[],[]] => 5
[[[.,[.,[[.,.],.]]],.],.] => [[[[],[]]],[],[]] => 4
[[[.,[[.,.],[.,.]]],.],.] => [[[],[[]]],[],[]] => 3
[[[.,[[.,[.,.]],.]],.],.] => [[[[]],[]],[],[]] => 4
[[[.,[[[.,.],.],.]],.],.] => [[[],[],[]],[],[]] => 3
[[[[.,.],[.,[.,.]]],.],.] => [[],[[[]]],[],[]] => 2
[[[[.,.],[[.,.],.]],.],.] => [[],[[],[]],[],[]] => 2
[[[[.,[.,.]],[.,.]],.],.] => [[[]],[[]],[],[]] => 3
[[[[[.,.],.],[.,.]],.],.] => [[],[],[[]],[],[]] => 2
[[[[.,[.,[.,.]]],.],.],.] => [[[[]]],[],[],[]] => 4
[[[[.,[[.,.],.]],.],.],.] => [[[],[]],[],[],[]] => 3
[[[[[.,.],[.,.]],.],.],.] => [[],[[]],[],[],[]] => 2
[[[[[.,[.,.]],.],.],.],.] => [[[]],[],[],[],[]] => 3
[[[[[[.,.],.],.],.],.],.] => [[],[],[],[],[],[]] => 2
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[[]]]]]]]] => 7
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[[],[]]]]]]] => 7
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[],[[]]]]]]] => 7
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[[[]],[]]]]]] => 7
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[[],[],[]]]]]] => 6
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[],[[[]]]]]]] => 7
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[],[[],[]]]]]] => 6
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[[]],[[]]]]]] => 7
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[],[],[[]]]]]] => 6
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[[[[]]],[]]]]] => 7
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [[[[[[],[]],[]]]]] => 6
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [[[[[],[[]],[]]]]] => 5
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [[[[[[]],[],[]]]]] => 6
[.,[.,[.,[[[[.,.],.],.],.]]]] => [[[[[],[],[],[]]]]] => 5
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[],[[[[]]]]]]] => 7
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [[[[],[[[],[]]]]]] => 6
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [[[[],[[],[[]]]]]] => 6
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [[[[],[[[]],[]]]]] => 5
[.,[.,[[.,.],[[[.,.],.],.]]]] => [[[[],[[],[],[]]]]] => 5
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[[[[]],[[[]]]]]] => 7
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [[[[[]],[[],[]]]]] => 6
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [[[[],[],[[[]]]]]] => 6
[.,[.,[[[.,.],.],[[.,.],.]]]] => [[[[],[],[[],[]]]]] => 5
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[[[]]],[[]]]]] => 7
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [[[[[],[]],[[]]]]] => 6
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [[[[],[[]],[[]]]]] => 5
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [[[[[]],[],[[]]]]] => 6
[.,[.,[[[[.,.],.],.],[.,.]]]] => [[[[],[],[],[[]]]]] => 5
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[[[[[[]]]],[]]]] => 7
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [[[[[[],[]]],[]]]] => 6
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [[[[[],[[]]],[]]]] => 5
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [[[[[[]],[]],[]]]] => 6
[.,[.,[[.,[[[.,.],.],.]],.]]] => [[[[[],[],[]],[]]]] => 5
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [[[[],[[[]]],[]]]] => 4
[.,[.,[[[.,.],[[.,.],.]],.]]] => [[[[],[[],[]],[]]]] => 4
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [[[[[]],[[]],[]]]] => 5
[.,[.,[[[[.,.],.],[.,.]],.]]] => [[[[],[],[[]],[]]]] => 4
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [[[[[[]]],[],[]]]] => 6
[.,[.,[[[.,[[.,.],.]],.],.]]] => [[[[[],[]],[],[]]]] => 5
[.,[.,[[[[.,.],[.,.]],.],.]]] => [[[[],[[]],[],[]]]] => 4
[.,[.,[[[[.,[.,.]],.],.],.]]] => [[[[[]],[],[],[]]]] => 5
[.,[.,[[[[[.,.],.],.],.],.]]] => [[[[],[],[],[],[]]]] => 4
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[[],[[[[[]]]]]]] => 7
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [[[],[[[[],[]]]]]] => 6
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [[[],[[[],[[]]]]]] => 6
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [[[],[[[[]],[]]]]] => 5
[.,[[.,.],[.,[[[.,.],.],.]]]] => [[[],[[[],[],[]]]]] => 5
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [[[],[[],[[[]]]]]] => 6
[.,[[.,.],[[.,.],[[.,.],.]]]] => [[[],[[],[[],[]]]]] => 5
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [[[],[[[]],[[]]]]] => 5
[.,[[.,.],[[[.,.],.],[.,.]]]] => [[[],[[],[],[[]]]]] => 5
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [[[],[[[[]]],[]]]] => 4
[.,[[.,.],[[.,[[.,.],.]],.]]] => [[[],[[[],[]],[]]]] => 4
[.,[[.,.],[[[.,.],[.,.]],.]]] => [[[],[[],[[]],[]]]] => 4
[.,[[.,.],[[[.,[.,.]],.],.]]] => [[[],[[[]],[],[]]]] => 4
[.,[[.,.],[[[[.,.],.],.],.]]] => [[[],[[],[],[],[]]]] => 4
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[]],[[[[]]]]]] => 7
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [[[[]],[[[],[]]]]] => 6
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [[[[]],[[],[[]]]]] => 6
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [[[[]],[[[]],[]]]] => 5
[.,[[.,[.,.]],[[[.,.],.],.]]] => [[[[]],[[],[],[]]]] => 5
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [[[],[],[[[[]]]]]] => 6
[.,[[[.,.],.],[.,[[.,.],.]]]] => [[[],[],[[[],[]]]]] => 5
[.,[[[.,.],.],[[.,.],[.,.]]]] => [[[],[],[[],[[]]]]] => 5
[.,[[[.,.],.],[[.,[.,.]],.]]] => [[[],[],[[[]],[]]]] => 4
[.,[[[.,.],.],[[[.,.],.],.]]] => [[[],[],[[],[],[]]]] => 4
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[[]]],[[[]]]]] => 7
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [[[[[]]],[[],[]]]] => 6
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [[[[],[]],[[[]]]]] => 6
[.,[[.,[[.,.],.]],[[.,.],.]]] => [[[[],[]],[[],[]]]] => 5
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [[[],[[]],[[[]]]]] => 5
[.,[[[.,.],[.,.]],[[.,.],.]]] => [[[],[[]],[[],[]]]] => 4
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [[[[]],[],[[[]]]]] => 6
[.,[[[.,[.,.]],.],[[.,.],.]]] => [[[[]],[],[[],[]]]] => 5
[.,[[[[.,.],.],.],[.,[.,.]]]] => [[[],[],[],[[[]]]]] => 5
[.,[[[[.,.],.],.],[[.,.],.]]] => [[[],[],[],[[],[]]]] => 4
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [[[[[[]]]],[[]]]] => 7
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [[[[[],[]]],[[]]]] => 6
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [[[[],[[]]],[[]]]] => 5
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [[[[[]],[]],[[]]]] => 6
[.,[[.,[[[.,.],.],.]],[.,.]]] => [[[[],[],[]],[[]]]] => 5
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [[[],[[[]]],[[]]]] => 4
[.,[[[.,.],[[.,.],.]],[.,.]]] => [[[],[[],[]],[[]]]] => 4
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [[[[]],[[]],[[]]]] => 5
[.,[[[[.,.],.],[.,.]],[.,.]]] => [[[],[],[[]],[[]]]] => 4
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [[[[[]]],[],[[]]]] => 6
[.,[[[.,[[.,.],.]],.],[.,.]]] => [[[[],[]],[],[[]]]] => 5
[.,[[[[.,.],[.,.]],.],[.,.]]] => [[[],[[]],[],[[]]]] => 4
[.,[[[[.,[.,.]],.],.],[.,.]]] => [[[[]],[],[],[[]]]] => 5
[.,[[[[[.,.],.],.],.],[.,.]]] => [[[],[],[],[],[[]]]] => 4
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[[[[[[]]]]],[]]] => 7
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [[[[[[],[]]]],[]]] => 6
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [[[[[],[[]]]],[]]] => 5
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [[[[[[]],[]]],[]]] => 6
[.,[[.,[.,[[[.,.],.],.]]],.]] => [[[[[],[],[]]],[]]] => 5
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [[[[],[[[]]]],[]]] => 4
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[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [[],[[[],[],[],[]]],[]] => 2
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [[],[[],[[[[]]]]],[]] => 2
[[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [[],[[],[[[],[]]]],[]] => 2
[[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [[],[[],[[],[[]]]],[]] => 2
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [[],[[],[[[]],[]]],[]] => 2
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [[],[[],[[],[],[]]],[]] => 2
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [[],[[[]],[[[]]]],[]] => 2
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [[],[[[]],[[],[]]],[]] => 2
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [[],[[],[],[[[]]]],[]] => 2
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [[],[[],[],[[],[]]],[]] => 2
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [[],[[[[]]],[[]]],[]] => 2
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [[],[[[],[]],[[]]],[]] => 2
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [[],[[],[[]],[[]]],[]] => 2
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [[],[[[]],[],[[]]],[]] => 2
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [[],[[],[],[],[[]]],[]] => 2
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [[],[[[[[]]]],[]],[]] => 2
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [[],[[[[],[]]],[]],[]] => 2
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [[],[[[],[[]]],[]],[]] => 2
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [[],[[[[]],[]],[]],[]] => 2
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [[],[[[],[],[]],[]],[]] => 2
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [[],[[],[[[]]],[]],[]] => 2
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [[],[[],[[],[]],[]],[]] => 2
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [[],[[[]],[[]],[]],[]] => 2
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [[],[[],[],[[]],[]],[]] => 2
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [[],[[[[]]],[],[]],[]] => 2
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [[],[[[],[]],[],[]],[]] => 2
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [[],[[],[[]],[],[]],[]] => 2
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [[],[[[]],[],[],[]],[]] => 2
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [[],[[],[],[],[],[]],[]] => 2
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[]],[[[[[]]]]],[]] => 3
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [[[]],[[[[],[]]]],[]] => 3
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [[[]],[[[],[[]]]],[]] => 3
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [[[]],[[[[]],[]]],[]] => 3
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [[[]],[[[],[],[]]],[]] => 3
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [[[]],[[],[[[]]]],[]] => 3
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [[[]],[[],[[],[]]],[]] => 3
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [[[]],[[[]],[[]]],[]] => 3
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [[[]],[[],[],[[]]],[]] => 3
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [[[]],[[[[]]],[]],[]] => 3
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [[[]],[[[],[]],[]],[]] => 3
[[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [[[]],[[],[[]],[]],[]] => 3
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [[[]],[[[]],[],[]],[]] => 3
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [[[]],[[],[],[],[]],[]] => 3
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[],[],[[[[[]]]]],[]] => 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
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [[],[],[],[[],[],[]],[]] => 2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[],[[[]]],[[[]]],[]] => 2
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [[],[[[]]],[[],[]],[]] => 2
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [[],[[],[]],[[[]]],[]] => 2
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[],[[],[]],[[],[]],[]] => 2
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[]],[[]],[[[]]],[]] => 3
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[]],[[]],[[],[]],[]] => 3
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [[],[],[[]],[[[]]],[]] => 2
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [[],[],[[]],[[],[]],[]] => 2
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[],[[]],[],[[[]]],[]] => 2
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [[],[[]],[],[[],[]],[]] => 2
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [[[]],[],[],[[[]]],[]] => 3
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [[[]],[],[],[[],[]],[]] => 3
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [[],[],[],[],[[[]]],[]] => 2
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [[],[],[],[],[[],[]],[]] => 2
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[],[[[[]]]],[[]],[]] => 2
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [[],[[[],[]]],[[]],[]] => 2
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [[],[[],[[]]],[[]],[]] => 2
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[],[[[]],[]],[[]],[]] => 2
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [[],[[],[],[]],[[]],[]] => 2
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[]],[[[]]],[[]],[]] => 3
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[]],[[],[]],[[]],[]] => 3
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [[],[],[[[]]],[[]],[]] => 2
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [[],[],[[],[]],[[]],[]] => 2
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [[],[[]],[[]],[[]],[]] => 2
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[]],[],[[]],[[]],[]] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [[],[],[],[[]],[[]],[]] => 2
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[],[[[]]],[],[[]],[]] => 2
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [[],[[],[]],[],[[]],[]] => 2
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[]],[[]],[],[[]],[]] => 3
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [[],[],[[]],[],[[]],[]] => 2
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[]]],[],[],[[]],[]] => 4
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [[[],[]],[],[],[[]],[]] => 3
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[],[[]],[],[],[[]],[]] => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [[[]],[],[],[],[[]],[]] => 3
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [[],[],[],[],[],[[]],[]] => 2
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[],[[[[[]]]]],[],[]] => 2
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [[],[[[[],[]]]],[],[]] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [[],[[[],[[]]]],[],[]] => 2
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [[],[[[[]],[]]],[],[]] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [[],[[[],[],[]]],[],[]] => 2
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [[],[[],[[[]]]],[],[]] => 2
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [[],[[],[[],[]]],[],[]] => 2
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [[],[[[]],[[]]],[],[]] => 2
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [[],[[],[],[[]]],[],[]] => 2
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [[],[[[[]]],[]],[],[]] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[],[[[],[]],[]],[],[]] => 2
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [[],[[],[[]],[]],[],[]] => 2
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [[],[[[]],[],[]],[],[]] => 2
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [[],[[],[],[],[]],[],[]] => 2
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[]],[[[[]]]],[],[]] => 3
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [[[]],[[[],[]]],[],[]] => 3
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [[[]],[[],[[]]],[],[]] => 3
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [[[]],[[[]],[]],[],[]] => 3
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[]],[[],[],[]],[],[]] => 3
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[],[],[[[[]]]],[],[]] => 2
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [[],[],[[[],[]]],[],[]] => 2
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [[],[],[[],[[]]],[],[]] => 2
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [[],[],[[[]],[]],[],[]] => 2
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [[],[],[[],[],[]],[],[]] => 2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [[],[[]],[[[]]],[],[]] => 2
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [[],[[]],[[],[]],[],[]] => 2
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[]],[],[[[]]],[],[]] => 3
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [[[]],[],[[],[]],[],[]] => 3
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [[],[],[],[[[]]],[],[]] => 2
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [[],[],[],[[],[]],[],[]] => 2
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[],[[[]]],[[]],[],[]] => 2
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [[],[[],[]],[[]],[],[]] => 2
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[]],[[]],[[]],[],[]] => 3
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [[],[],[[]],[[]],[],[]] => 2
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[]]],[],[[]],[],[]] => 4
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [[[],[]],[],[[]],[],[]] => 3
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[],[[]],[],[[]],[],[]] => 2
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [[[]],[],[],[[]],[],[]] => 3
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [[],[],[],[],[[]],[],[]] => 2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [[],[[[[]]]],[],[],[]] => 2
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [[],[[[],[]]],[],[],[]] => 2
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [[],[[],[[]]],[],[],[]] => 2
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [[],[[[]],[]],[],[],[]] => 2
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [[],[[],[],[]],[],[],[]] => 2
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[]],[[[]]],[],[],[]] => 3
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [[[]],[[],[]],[],[],[]] => 3
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [[],[],[[[]]],[],[],[]] => 2
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [[],[],[[],[]],[],[],[]] => 2
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [[],[[]],[[]],[],[],[]] => 2
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [[[]],[],[[]],[],[],[]] => 3
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [[],[],[],[[]],[],[],[]] => 2
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[],[[[]]],[],[],[],[]] => 2
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [[],[[],[]],[],[],[],[]] => 2
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[]],[[]],[],[],[],[]] => 3
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [[],[],[[]],[],[],[],[]] => 2
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [[[[]]],[],[],[],[],[]] => 4
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [[[],[]],[],[],[],[],[]] => 3
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [[],[[]],[],[],[],[],[]] => 2
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [[[]],[],[],[],[],[],[]] => 3
[[[[[[[[.,.],.],.],.],.],.],.],.] => [[],[],[],[],[],[],[],[]] => 2
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,4 2,5,7 5,12,14,11 14,33,39,30,16 42,98,117,95,55,22
$F_{1} = q$
$F_{2} = 2\ q^{2}$
$F_{3} = q^{2} + 4\ q^{3}$
$F_{4} = 2\ q^{2} + 5\ q^{3} + 7\ q^{4}$
$F_{5} = 5\ q^{2} + 12\ q^{3} + 14\ q^{4} + 11\ q^{5}$
$F_{6} = 14\ q^{2} + 33\ q^{3} + 39\ q^{4} + 30\ q^{5} + 16\ q^{6}$
$F_{7} = 42\ q^{2} + 98\ q^{3} + 117\ q^{4} + 95\ q^{5} + 55\ q^{6} + 22\ q^{7}$
Description
The length of the boundary minus the length of the trunk of an ordered tree.
This is the size of the set of edges which are either on the left most path or on the right most path from the root.
This is the size of the set of edges which are either on the left most path or on the right most path from the root.
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 $y$.
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