Identifier
Values
[[]] => [1,0] => 0
[[],[]] => [1,0,1,0] => 0
[[[]]] => [1,1,0,0] => 1
[[],[],[]] => [1,0,1,0,1,0] => 0
[[],[[]]] => [1,0,1,1,0,0] => 1
[[[]],[]] => [1,1,0,0,1,0] => 1
[[[],[]]] => [1,1,0,1,0,0] => 2
[[[[]]]] => [1,1,1,0,0,0] => 1
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 0
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => 1
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => 1
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => 1
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => 1
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 1
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => 3
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => 2
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => 2
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => 1
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 2
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 0
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => 1
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => 1
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 1
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 3
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => 2
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 2
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 3
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 1
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 3
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 3
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => 2
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => 2
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => 1
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 2
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 4
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 3
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 3
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => 3
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => 3
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => 2
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => 2
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => 3
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => 1
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 2
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 2
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 3
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 2
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 4
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 4
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 4
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 4
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
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Description
The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.