Identifier
Values
[[]] => [1,0] => 1
[[],[]] => [1,0,1,0] => 1
[[[]]] => [1,1,0,0] => 2
[[],[],[]] => [1,0,1,0,1,0] => 1
[[],[[]]] => [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] => 3
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 1
[[],[],[[]]] => [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] => 1
[[],[[[]]]] => [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] => 1
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 1
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => 2
[[[],[[]]]] => [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] => 3
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 4
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 1
[[],[],[],[[]]] => [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] => 1
[[],[],[[[]]]] => [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] => 1
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => 1
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 1
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 1
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => 1
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => 1
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 1
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 1
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 1
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => 1
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => 1
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => 1
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 1
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 2
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 2
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => 2
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => 2
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => 3
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => 2
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => 2
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => 3
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 3
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 3
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 4
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 5
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[],[],[],[],[[]]] => [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] => 1
[[],[],[],[[[]]]] => [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] => 1
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[],[[[]]],[]] => [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] => 1
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[],[[[],[]]]] => [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] => 1
[[],[[]],[],[],[]] => [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] => 1
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[[[]]],[],[]] => [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] => 1
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[[],[[[],[]]],[]] => [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] => 1
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
>>> 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] => 1
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[[]],[],[],[],[]] => [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] => 1
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[[]],[[[],[]]]] => [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] => 2
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[[]]],[],[],[]] => [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] => 1
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[[[[],[]]],[],[]] => [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] => 1
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[[[],[]]],[[]]] => [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] => 2
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[[[[],[],[]]],[]] => [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] => 1
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[[[],[[],[],[]]]] => [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] => 2
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[[[]],[[[]]]]] => [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] => 2
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[[[[]]],[[]]]] => [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] => 2
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[[[],[[],[]]]]] => [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] => 3
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
[[[[[],[]],[]]]] => [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] => 3
[[[[[],[],[]]]]] => [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] => 4
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
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searching the database for statistics with the same generating function
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Description
The minimal height of a peak of a Dyck path.
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.