edit this statistic or download as text // json
Identifier
Values
[.,.] => 0
[.,[.,.]] => 0
[[.,.],.] => 0
[.,[.,[.,.]]] => 0
[.,[[.,.],.]] => 0
[[.,.],[.,.]] => 0
[[.,[.,.]],.] => 0
[[[.,.],.],.] => 0
[.,[.,[.,[.,.]]]] => 0
[.,[.,[[.,.],.]]] => 0
[.,[[.,.],[.,.]]] => 0
[.,[[.,[.,.]],.]] => 0
[.,[[[.,.],.],.]] => 0
[[.,.],[.,[.,.]]] => 0
[[.,.],[[.,.],.]] => 0
[[.,[.,.]],[.,.]] => 0
[[[.,.],.],[.,.]] => 0
[[.,[.,[.,.]]],.] => 0
[[.,[[.,.],.]],.] => 0
[[[.,.],[.,.]],.] => 0
[[[.,[.,.]],.],.] => 0
[[[[.,.],.],.],.] => 0
[.,[.,[.,[.,[.,.]]]]] => 0
[.,[.,[.,[[.,.],.]]]] => 0
[.,[.,[[.,.],[.,.]]]] => 0
[.,[.,[[.,[.,.]],.]]] => 0
[.,[.,[[[.,.],.],.]]] => 0
[.,[[.,.],[.,[.,.]]]] => 0
[.,[[.,.],[[.,.],.]]] => 0
[.,[[.,[.,.]],[.,.]]] => 0
[.,[[[.,.],.],[.,.]]] => 0
[.,[[.,[.,[.,.]]],.]] => 0
[.,[[.,[[.,.],.]],.]] => 0
[.,[[[.,.],[.,.]],.]] => 0
[.,[[[.,[.,.]],.],.]] => 0
[.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[.,[.,.]]]] => 0
[[.,.],[.,[[.,.],.]]] => 0
[[.,.],[[.,.],[.,.]]] => 0
[[.,.],[[.,[.,.]],.]] => 0
[[.,.],[[[.,.],.],.]] => 0
[[.,[.,.]],[.,[.,.]]] => 0
[[.,[.,.]],[[.,.],.]] => 0
[[[.,.],.],[.,[.,.]]] => 0
[[[.,.],.],[[.,.],.]] => 0
[[.,[.,[.,.]]],[.,.]] => 0
[[.,[[.,.],.]],[.,.]] => 0
[[[.,.],[.,.]],[.,.]] => 0
[[[.,[.,.]],.],[.,.]] => 0
[[[[.,.],.],.],[.,.]] => 0
[[.,[.,[.,[.,.]]]],.] => 0
[[.,[.,[[.,.],.]]],.] => 0
[[.,[[.,.],[.,.]]],.] => 0
[[.,[[.,[.,.]],.]],.] => 0
[[.,[[[.,.],.],.]],.] => 0
[[[.,.],[.,[.,.]]],.] => 0
[[[.,.],[[.,.],.]],.] => 0
[[[.,[.,.]],[.,.]],.] => 0
[[[[.,.],.],[.,.]],.] => 0
[[[.,[.,[.,.]]],.],.] => 0
[[[.,[[.,.],.]],.],.] => 0
[[[[.,.],[.,.]],.],.] => 0
[[[[.,[.,.]],.],.],.] => 0
[[[[[.,.],.],.],.],.] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => 0
[.,[.,[.,[[.,.],[.,.]]]]] => 0
[.,[.,[.,[[.,[.,.]],.]]]] => 0
[.,[.,[.,[[[.,.],.],.]]]] => 0
[.,[.,[[.,.],[.,[.,.]]]]] => 0
[.,[.,[[.,.],[[.,.],.]]]] => 0
[.,[.,[[.,[.,.]],[.,.]]]] => 0
[.,[.,[[[.,.],.],[.,.]]]] => 0
[.,[.,[[.,[.,[.,.]]],.]]] => 0
[.,[.,[[.,[[.,.],.]],.]]] => 0
[.,[.,[[[.,.],[.,.]],.]]] => 0
[.,[.,[[[.,[.,.]],.],.]]] => 0
[.,[.,[[[[.,.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => 0
[.,[[.,.],[.,[[.,.],.]]]] => 0
[.,[[.,.],[[.,.],[.,.]]]] => 0
[.,[[.,.],[[.,[.,.]],.]]] => 0
[.,[[.,.],[[[.,.],.],.]]] => 0
[.,[[.,[.,.]],[.,[.,.]]]] => 0
[.,[[.,[.,.]],[[.,.],.]]] => 0
[.,[[[.,.],.],[.,[.,.]]]] => 0
[.,[[[.,.],.],[[.,.],.]]] => 0
[.,[[.,[.,[.,.]]],[.,.]]] => 0
[.,[[.,[[.,.],.]],[.,.]]] => 0
[.,[[[.,.],[.,.]],[.,.]]] => 0
[.,[[[.,[.,.]],.],[.,.]]] => 0
[.,[[[[.,.],.],.],[.,.]]] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => 0
[.,[[.,[.,[[.,.],.]]],.]] => 0
[.,[[.,[[.,.],[.,.]]],.]] => 0
[.,[[.,[[.,[.,.]],.]],.]] => 0
[.,[[.,[[[.,.],.],.]],.]] => 0
[.,[[[.,.],[.,[.,.]]],.]] => 0
[.,[[[.,.],[[.,.],.]],.]] => 0
[.,[[[.,[.,.]],[.,.]],.]] => 0
[.,[[[[.,.],.],[.,.]],.]] => 1
>>> Load all 625 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => 0
[.,[[[.,[[.,.],.]],.],.]] => 0
[.,[[[[.,.],[.,.]],.],.]] => 1
[.,[[[[.,[.,.]],.],.],.]] => 1
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 0
[[.,.],[.,[.,[[.,.],.]]]] => 0
[[.,.],[.,[[.,.],[.,.]]]] => 0
[[.,.],[.,[[.,[.,.]],.]]] => 0
[[.,.],[.,[[[.,.],.],.]]] => 0
[[.,.],[[.,.],[.,[.,.]]]] => 0
[[.,.],[[.,.],[[.,.],.]]] => 0
[[.,.],[[.,[.,.]],[.,.]]] => 0
[[.,.],[[[.,.],.],[.,.]]] => 0
[[.,.],[[.,[.,[.,.]]],.]] => 0
[[.,.],[[.,[[.,.],.]],.]] => 0
[[.,.],[[[.,.],[.,.]],.]] => 0
[[.,.],[[[.,[.,.]],.],.]] => 0
[[.,.],[[[[.,.],.],.],.]] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => 0
[[.,[.,.]],[.,[[.,.],.]]] => 0
[[.,[.,.]],[[.,.],[.,.]]] => 0
[[.,[.,.]],[[.,[.,.]],.]] => 0
[[.,[.,.]],[[[.,.],.],.]] => 0
[[[.,.],.],[.,[.,[.,.]]]] => 0
[[[.,.],.],[.,[[.,.],.]]] => 0
[[[.,.],.],[[.,.],[.,.]]] => 0
[[[.,.],.],[[.,[.,.]],.]] => 0
[[[.,.],.],[[[.,.],.],.]] => 0
[[.,[.,[.,.]]],[.,[.,.]]] => 0
[[.,[.,[.,.]]],[[.,.],.]] => 0
[[.,[[.,.],.]],[.,[.,.]]] => 0
[[.,[[.,.],.]],[[.,.],.]] => 0
[[[.,.],[.,.]],[.,[.,.]]] => 0
[[[.,.],[.,.]],[[.,.],.]] => 0
[[[.,[.,.]],.],[.,[.,.]]] => 0
[[[.,[.,.]],.],[[.,.],.]] => 0
[[[[.,.],.],.],[.,[.,.]]] => 0
[[[[.,.],.],.],[[.,.],.]] => 0
[[.,[.,[.,[.,.]]]],[.,.]] => 0
[[.,[.,[[.,.],.]]],[.,.]] => 0
[[.,[[.,.],[.,.]]],[.,.]] => 0
[[.,[[.,[.,.]],.]],[.,.]] => 0
[[.,[[[.,.],.],.]],[.,.]] => 0
[[[.,.],[.,[.,.]]],[.,.]] => 0
[[[.,.],[[.,.],.]],[.,.]] => 0
[[[.,[.,.]],[.,.]],[.,.]] => 0
[[[[.,.],.],[.,.]],[.,.]] => 0
[[[.,[.,[.,.]]],.],[.,.]] => 0
[[[.,[[.,.],.]],.],[.,.]] => 0
[[[[.,.],[.,.]],.],[.,.]] => 0
[[[[.,[.,.]],.],.],[.,.]] => 0
[[[[[.,.],.],.],.],[.,.]] => 0
[[.,[.,[.,[.,[.,.]]]]],.] => 0
[[.,[.,[.,[[.,.],.]]]],.] => 0
[[.,[.,[[.,.],[.,.]]]],.] => 0
[[.,[.,[[.,[.,.]],.]]],.] => 0
[[.,[.,[[[.,.],.],.]]],.] => 0
[[.,[[.,.],[.,[.,.]]]],.] => 0
[[.,[[.,.],[[.,.],.]]],.] => 0
[[.,[[.,[.,.]],[.,.]]],.] => 0
[[.,[[[.,.],.],[.,.]]],.] => 0
[[.,[[.,[.,[.,.]]],.]],.] => 0
[[.,[[.,[[.,.],.]],.]],.] => 0
[[.,[[[.,.],[.,.]],.]],.] => 0
[[.,[[[.,[.,.]],.],.]],.] => 0
[[.,[[[[.,.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,.]]]],.] => 0
[[[.,.],[.,[[.,.],.]]],.] => 0
[[[.,.],[[.,.],[.,.]]],.] => 0
[[[.,.],[[.,[.,.]],.]],.] => 0
[[[.,.],[[[.,.],.],.]],.] => 0
[[[.,[.,.]],[.,[.,.]]],.] => 0
[[[.,[.,.]],[[.,.],.]],.] => 0
[[[[.,.],.],[.,[.,.]]],.] => 0
[[[[.,.],.],[[.,.],.]],.] => 0
[[[.,[.,[.,.]]],[.,.]],.] => 0
[[[.,[[.,.],.]],[.,.]],.] => 0
[[[[.,.],[.,.]],[.,.]],.] => 0
[[[[.,[.,.]],.],[.,.]],.] => 0
[[[[[.,.],.],.],[.,.]],.] => 0
[[[.,[.,[.,[.,.]]]],.],.] => 0
[[[.,[.,[[.,.],.]]],.],.] => 0
[[[.,[[.,.],[.,.]]],.],.] => 0
[[[.,[[.,[.,.]],.]],.],.] => 0
[[[.,[[[.,.],.],.]],.],.] => 0
[[[[.,.],[.,[.,.]]],.],.] => 0
[[[[.,.],[[.,.],.]],.],.] => 0
[[[[.,[.,.]],[.,.]],.],.] => 0
[[[[[.,.],.],[.,.]],.],.] => 0
[[[[.,[.,[.,.]]],.],.],.] => 0
[[[[.,[[.,.],.]],.],.],.] => 0
[[[[[.,.],[.,.]],.],.],.] => 0
[[[[[.,[.,.]],.],.],.],.] => 0
[[[[[[.,.],.],.],.],.],.] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 0
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 0
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 0
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 0
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 0
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 0
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 0
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 0
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 0
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 0
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 0
[.,[.,[[.,.],[[[.,.],.],.]]]] => 0
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 0
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 0
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 0
[.,[.,[[[.,.],.],[[.,.],.]]]] => 0
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 0
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 0
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 0
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 0
[.,[.,[[[[.,.],.],.],[.,.]]]] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 0
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 0
[.,[.,[[[.,.],[[.,.],.]],.]]] => 0
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 0
[.,[.,[[[[.,.],.],[.,.]],.]]] => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 0
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 0
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 0
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 0
[.,[[.,.],[.,[[[.,.],.],.]]]] => 0
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 0
[.,[[.,.],[[.,.],[[.,.],.]]]] => 0
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 0
[.,[[.,.],[[[.,.],.],[.,.]]]] => 0
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 0
[.,[[.,.],[[.,[[.,.],.]],.]]] => 0
[.,[[.,.],[[[.,.],[.,.]],.]]] => 0
[.,[[.,.],[[[.,[.,.]],.],.]]] => 0
[.,[[.,.],[[[[.,.],.],.],.]]] => 1
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 0
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 0
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 0
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 0
[.,[[.,[.,.]],[[[.,.],.],.]]] => 0
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 0
[.,[[[.,.],.],[.,[[.,.],.]]]] => 0
[.,[[[.,.],.],[[.,.],[.,.]]]] => 0
[.,[[[.,.],.],[[.,[.,.]],.]]] => 0
[.,[[[.,.],.],[[[.,.],.],.]]] => 0
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 0
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 0
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 0
[.,[[.,[[.,.],.]],[[.,.],.]]] => 0
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 0
[.,[[[.,.],[.,.]],[[.,.],.]]] => 0
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 0
[.,[[[.,[.,.]],.],[[.,.],.]]] => 0
[.,[[[[.,.],.],.],[.,[.,.]]]] => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 0
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 0
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 0
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 0
[.,[[.,[[[.,.],.],.]],[.,.]]] => 0
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 0
[.,[[[.,.],[[.,.],.]],[.,.]]] => 0
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 0
[.,[[[[.,.],.],[.,.]],[.,.]]] => 1
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 0
[.,[[[.,[[.,.],.]],.],[.,.]]] => 0
[.,[[[[.,.],[.,.]],.],[.,.]]] => 1
[.,[[[[.,[.,.]],.],.],[.,.]]] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 0
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 0
[.,[[.,[[.,.],[[.,.],.]]],.]] => 0
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 0
[.,[[.,[[[.,.],.],[.,.]]],.]] => 0
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => 0
[.,[[[.,.],[[.,.],[.,.]]],.]] => 0
[.,[[[.,.],[[.,[.,.]],.]],.]] => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => 0
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 0
[.,[[[.,[.,.]],[[.,.],.]],.]] => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => 1
[.,[[[[.,.],.],[[.,.],.]],.]] => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => 1
[.,[[[[.,[.,.]],.],[.,.]],.]] => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => 1
[.,[[[[.,[.,.]],[.,.]],.],.]] => 1
[.,[[[[[.,.],.],[.,.]],.],.]] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 0
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 0
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 0
[[.,.],[.,[.,[[[.,.],.],.]]]] => 0
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 0
[[.,.],[.,[[.,.],[[.,.],.]]]] => 0
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 0
[[.,.],[.,[[[.,.],.],[.,.]]]] => 0
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 0
[[.,.],[.,[[.,[[.,.],.]],.]]] => 0
[[.,.],[.,[[[.,.],[.,.]],.]]] => 0
[[.,.],[.,[[[.,[.,.]],.],.]]] => 0
[[.,.],[.,[[[[.,.],.],.],.]]] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 0
[[.,.],[[.,.],[.,[[.,.],.]]]] => 0
[[.,.],[[.,.],[[.,.],[.,.]]]] => 0
[[.,.],[[.,.],[[.,[.,.]],.]]] => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => 0
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 0
[[.,.],[[.,[.,.]],[[.,.],.]]] => 0
[[.,.],[[[.,.],.],[.,[.,.]]]] => 0
[[.,.],[[[.,.],.],[[.,.],.]]] => 0
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 0
[[.,.],[[.,[[.,.],.]],[.,.]]] => 0
[[.,.],[[[.,.],[.,.]],[.,.]]] => 0
[[.,.],[[[.,[.,.]],.],[.,.]]] => 0
[[.,.],[[[[.,.],.],.],[.,.]]] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 0
[[.,.],[[.,[.,[[.,.],.]]],.]] => 0
[[.,.],[[.,[[.,.],[.,.]]],.]] => 0
[[.,.],[[.,[[.,[.,.]],.]],.]] => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => 0
[[.,.],[[[.,.],[.,[.,.]]],.]] => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => 0
[[.,.],[[[.,[.,.]],[.,.]],.]] => 0
[[.,.],[[[[.,.],.],[.,.]],.]] => 1
[[.,.],[[[.,[.,[.,.]]],.],.]] => 0
[[.,.],[[[.,[[.,.],.]],.],.]] => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => 1
[[.,.],[[[[.,[.,.]],.],.],.]] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 0
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 0
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 0
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 0
[[.,[.,.]],[.,[[[.,.],.],.]]] => 0
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 0
[[.,[.,.]],[[.,.],[[.,.],.]]] => 0
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 0
[[.,[.,.]],[[[.,.],.],[.,.]]] => 0
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 0
[[.,[.,.]],[[.,[[.,.],.]],.]] => 0
[[.,[.,.]],[[[.,.],[.,.]],.]] => 0
[[.,[.,.]],[[[.,[.,.]],.],.]] => 0
[[.,[.,.]],[[[[.,.],.],.],.]] => 1
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] => 0
[[[.,.],.],[.,[[.,.],[.,.]]]] => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => 0
[[[.,.],.],[[.,.],[.,[.,.]]]] => 0
[[[.,.],.],[[.,.],[[.,.],.]]] => 0
[[[.,.],.],[[.,[.,.]],[.,.]]] => 0
[[[.,.],.],[[[.,.],.],[.,.]]] => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] => 0
[[[.,.],.],[[.,[[.,.],.]],.]] => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => 0
[[[.,.],.],[[[[.,.],.],.],.]] => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 0
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 0
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 0
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 0
[[.,[.,[.,.]]],[[[.,.],.],.]] => 0
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 0
[[.,[[.,.],.]],[.,[[.,.],.]]] => 0
[[.,[[.,.],.]],[[.,.],[.,.]]] => 0
[[.,[[.,.],.]],[[.,[.,.]],.]] => 0
[[.,[[.,.],.]],[[[.,.],.],.]] => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 0
[[[.,.],[.,.]],[.,[[.,.],.]]] => 0
[[[.,.],[.,.]],[[.,.],[.,.]]] => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => 0
[[[.,.],[.,.]],[[[.,.],.],.]] => 0
[[[.,[.,.]],.],[.,[.,[.,.]]]] => 0
[[[.,[.,.]],.],[.,[[.,.],.]]] => 0
[[[.,[.,.]],.],[[.,.],[.,.]]] => 0
[[[.,[.,.]],.],[[.,[.,.]],.]] => 0
[[[.,[.,.]],.],[[[.,.],.],.]] => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[[[[.,.],.],.],[.,[[.,.],.]]] => 0
[[[[.,.],.],.],[[.,.],[.,.]]] => 0
[[[[.,.],.],.],[[.,[.,.]],.]] => 0
[[[[.,.],.],.],[[[.,.],.],.]] => 0
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => 0
[[.,[.,[.,[.,.]]]],[[.,.],.]] => 0
[[.,[.,[[.,.],.]]],[.,[.,.]]] => 0
[[.,[.,[[.,.],.]]],[[.,.],.]] => 0
[[.,[[.,.],[.,.]]],[.,[.,.]]] => 0
[[.,[[.,.],[.,.]]],[[.,.],.]] => 0
[[.,[[.,[.,.]],.]],[.,[.,.]]] => 0
[[.,[[.,[.,.]],.]],[[.,.],.]] => 0
[[.,[[[.,.],.],.]],[.,[.,.]]] => 0
[[.,[[[.,.],.],.]],[[.,.],.]] => 0
[[[.,.],[.,[.,.]]],[.,[.,.]]] => 0
[[[.,.],[.,[.,.]]],[[.,.],.]] => 0
[[[.,.],[[.,.],.]],[.,[.,.]]] => 0
[[[.,.],[[.,.],.]],[[.,.],.]] => 0
[[[.,[.,.]],[.,.]],[.,[.,.]]] => 0
[[[.,[.,.]],[.,.]],[[.,.],.]] => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] => 0
[[[[.,.],.],[.,.]],[[.,.],.]] => 0
[[[.,[.,[.,.]]],.],[.,[.,.]]] => 0
[[[.,[.,[.,.]]],.],[[.,.],.]] => 0
[[[.,[[.,.],.]],.],[.,[.,.]]] => 0
[[[.,[[.,.],.]],.],[[.,.],.]] => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] => 0
[[[[.,.],[.,.]],.],[[.,.],.]] => 0
[[[[.,[.,.]],.],.],[.,[.,.]]] => 0
[[[[.,[.,.]],.],.],[[.,.],.]] => 0
[[[[[.,.],.],.],.],[.,[.,.]]] => 0
[[[[[.,.],.],.],.],[[.,.],.]] => 0
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => 0
[[.,[.,[.,[[.,.],.]]]],[.,.]] => 0
[[.,[.,[[.,.],[.,.]]]],[.,.]] => 0
[[.,[.,[[.,[.,.]],.]]],[.,.]] => 0
[[.,[.,[[[.,.],.],.]]],[.,.]] => 0
[[.,[[.,.],[.,[.,.]]]],[.,.]] => 0
[[.,[[.,.],[[.,.],.]]],[.,.]] => 0
[[.,[[.,[.,.]],[.,.]]],[.,.]] => 0
[[.,[[[.,.],.],[.,.]]],[.,.]] => 0
[[.,[[.,[.,[.,.]]],.]],[.,.]] => 0
[[.,[[.,[[.,.],.]],.]],[.,.]] => 0
[[.,[[[.,.],[.,.]],.]],[.,.]] => 0
[[.,[[[.,[.,.]],.],.]],[.,.]] => 0
[[.,[[[[.,.],.],.],.]],[.,.]] => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] => 0
[[[.,.],[[.,.],[.,.]]],[.,.]] => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] => 0
[[[.,.],[[[.,.],.],.]],[.,.]] => 0
[[[.,[.,.]],[.,[.,.]]],[.,.]] => 0
[[[.,[.,.]],[[.,.],.]],[.,.]] => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => 0
[[[[.,.],.],[[.,.],.]],[.,.]] => 0
[[[.,[.,[.,.]]],[.,.]],[.,.]] => 0
[[[.,[[.,.],.]],[.,.]],[.,.]] => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => 0
[[[.,[.,[.,[.,.]]]],.],[.,.]] => 0
[[[.,[.,[[.,.],.]]],.],[.,.]] => 0
[[[.,[[.,.],[.,.]]],.],[.,.]] => 0
[[[.,[[.,[.,.]],.]],.],[.,.]] => 0
[[[.,[[[.,.],.],.]],.],[.,.]] => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => 0
[[[[.,.],[[.,.],.]],.],[.,.]] => 0
[[[[.,[.,.]],[.,.]],.],[.,.]] => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => 0
[[[[.,[.,[.,.]]],.],.],[.,.]] => 0
[[[[.,[[.,.],.]],.],.],[.,.]] => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => 0
[[[[[.,[.,.]],.],.],.],[.,.]] => 0
[[[[[[.,.],.],.],.],.],[.,.]] => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] => 0
[[.,[.,[[.,[.,.]],[.,.]]]],.] => 0
[[.,[.,[[[.,.],.],[.,.]]]],.] => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => 0
[[.,[.,[[[.,[.,.]],.],.]]],.] => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] => 0
[[.,[[.,.],[[.,.],[.,.]]]],.] => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] => 0
[[.,[[.,.],[[[.,.],.],.]]],.] => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] => 0
[[.,[[.,[.,.]],[[.,.],.]]],.] => 0
[[.,[[[.,.],.],[.,[.,.]]]],.] => 0
[[.,[[[.,.],.],[[.,.],.]]],.] => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] => 0
[[.,[[.,[[.,.],.]],[.,.]]],.] => 0
[[.,[[[.,.],[.,.]],[.,.]]],.] => 0
[[.,[[[.,[.,.]],.],[.,.]]],.] => 0
[[.,[[[[.,.],.],.],[.,.]]],.] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => 0
[[.,[[[.,.],[[.,.],.]],.]],.] => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] => 0
[[[.,.],[.,[[.,[.,.]],.]]],.] => 0
[[[.,.],[.,[[[.,.],.],.]]],.] => 0
[[[.,.],[[.,.],[.,[.,.]]]],.] => 0
[[[.,.],[[.,.],[[.,.],.]]],.] => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] => 0
[[[.,.],[[[.,.],.],[.,.]]],.] => 0
[[[.,.],[[.,[.,[.,.]]],.]],.] => 0
[[[.,.],[[.,[[.,.],.]],.]],.] => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => 0
[[[.,.],[[[[.,.],.],.],.]],.] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => 0
[[[.,[.,.]],[.,[[.,.],.]]],.] => 0
[[[.,[.,.]],[[.,.],[.,.]]],.] => 0
[[[.,[.,.]],[[.,[.,.]],.]],.] => 0
[[[.,[.,.]],[[[.,.],.],.]],.] => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => 0
[[[[.,.],.],[.,[[.,.],.]]],.] => 0
[[[[.,.],.],[[.,.],[.,.]]],.] => 0
[[[[.,.],.],[[.,[.,.]],.]],.] => 0
[[[[.,.],.],[[[.,.],.],.]],.] => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] => 0
[[[.,[.,[.,.]]],[[.,.],.]],.] => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] => 0
[[[.,[[.,.],.]],[[.,.],.]],.] => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => 0
[[[[.,.],[.,.]],[[.,.],.]],.] => 0
[[[[.,[.,.]],.],[.,[.,.]]],.] => 0
[[[[.,[.,.]],.],[[.,.],.]],.] => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => 0
[[[[[.,.],.],.],[[.,.],.]],.] => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] => 0
[[[.,[[.,.],[.,.]]],[.,.]],.] => 0
[[[.,[[.,[.,.]],.]],[.,.]],.] => 0
[[[.,[[[.,.],.],.]],[.,.]],.] => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => 0
[[[[.,.],[[.,.],.]],[.,.]],.] => 0
[[[[.,[.,.]],[.,.]],[.,.]],.] => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => 0
[[[[.,[.,[.,.]]],.],[.,.]],.] => 0
[[[[.,[[.,.],.]],.],[.,.]],.] => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => 0
[[[[[.,[.,.]],.],.],[.,.]],.] => 0
[[[[[[.,.],.],.],.],[.,.]],.] => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => 0
[[[.,[[.,.],[[.,.],.]]],.],.] => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] => 0
[[[.,[[[.,.],.],[.,.]]],.],.] => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => 0
[[[.,[[[.,[.,.]],.],.]],.],.] => 0
[[[.,[[[[.,.],.],.],.]],.],.] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => 0
[[[[.,.],[[[.,.],.],.]],.],.] => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] => 0
[[[[.,[.,.]],[[.,.],.]],.],.] => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => 0
[[[[[.,.],.],[[.,.],.]],.],.] => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => 0
[[[[[[.,.],.],.],[.,.]],.],.] => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => 0
[[[[.,[[.,[.,.]],.]],.],.],.] => 0
[[[[.,[[[.,.],.],.]],.],.],.] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => 0
[[[[[.,.],[[.,.],.]],.],.],.] => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => 0
[[[[[.,[[.,.],.]],.],.],.],.] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => 0
[[[[[[.,[.,.]],.],.],.],.],.] => 0
[[[[[[[.,.],.],.],.],.],.],.] => 0
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 occurrences of the contiguous pattern [.,[[[[.,.],.],.],.]] in a binary tree.
oeis:A159772 counts binary trees avoiding this pattern.
References
[1] Rowland, E. S. Pattern avoidance in binary trees MathSciNet:2645188 arXiv:0809.0488
Code
(* in Mathematica *)
tree = {{{{}, {}}, {{}, {}}}, {{{}, {}}, {{}, {}}}};
Count[tree, {{___}, {{{{{___}, {___}}, {___}}, {___}}, {___}}}, {0, Infinity}]

Created
Jun 18, 2013 at 18:58 by Eric Rowland
Updated
Oct 17, 2015 at 11:06 by Christian Stump