Processing math: 100%

Identifier
Values
[1] => [1,0] => [.,.] => [.,.] => 0
[1,1] => [1,0,1,0] => [.,[.,.]] => [[.,.],.] => 0
[2] => [1,1,0,0] => [[.,.],.] => [.,[.,.]] => 0
[1,1,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => [[.,.],[.,.]] => 0
[1,2] => [1,0,1,1,0,0] => [.,[[.,.],.]] => [[.,[.,.]],.] => 0
[2,1] => [1,1,0,0,1,0] => [[.,[.,.]],.] => [.,[.,[.,.]]] => 0
[3] => [1,1,1,0,0,0] => [[.,.],[.,.]] => [[[.,.],.],.] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [[.,.],[.,[.,.]]] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [[.,.],[[.,.],.]] => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],.]] => [[.,[.,[.,.]]],.] => 0
[1,3] => [1,0,1,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [[.,[.,.]],[.,.]] => 0
[2,1,1] => [1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],.] => [.,[.,[.,[.,.]]]] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],.] => [.,[.,[[.,.],.]]] => 0
[3,1] => [1,1,1,0,0,0,1,0] => [[.,.],[.,[.,.]]] => [[[.,.],.],[.,.]] => 0
[4] => [1,1,1,1,0,0,0,0] => [[[.,.],.],[.,.]] => [[[[.,.],.],.],.] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [[.,.],[.,[.,[.,.]]]] => 0
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [[.,.],[.,[[.,.],.]]] => 0
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,[.,.]],.]]] => [[.,.],[[.,[.,.]],.]] => 0
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [[.,.],[[.,.],[.,.]]] => 0
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],.]] => [[.,[.,[.,[.,.]]]],.] => 0
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],.]] => [[.,[.,[[.,.],.]]],.] => 0
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [[.,[.,.]],[.,[.,.]]] => 0
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,.]]] => [[.,[[.,.],.]],[.,.]] => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [.,[.,[.,[.,[.,.]]]]] => 0
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],.] => [.,[.,[.,[[.,.],.]]]] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [.,[.,[[.,[.,.]],.]]] => 0
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],.] => [.,[.,[[.,.],[.,.]]]] => 0
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => [[[.,.],.],[.,[.,.]]] => 0
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [[[.,.],.],[[.,.],.]] => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[.,.]]] => [[[[.,.],.],.],[.,.]] => 0
[5] => [1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,.]] => [[[[.,.],[.,.]],.],.] => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [[.,.],[.,[[.,[.,.]],.]]] => 0
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => 0
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [[.,.],[[.,[.,[.,.]]],.]] => 0
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [[.,.],[[.,[[.,.],.]],.]] => 0
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => 0
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [[.,.],[[[.,.],.],[.,.]]] => 0
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [[.,[.,[.,[.,[.,.]]]]],.] => 0
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],.]] => [[.,[.,[[.,[.,.]],.]]],.] => 0
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [[.,[.,[[.,.],[.,.]]]],.] => 0
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => 0
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [[.,[.,.]],[.,[[.,.],.]]] => 0
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [[.,[[.,.],.]],[.,[.,.]]] => 0
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [[.,[[.,.],[.,.]]],[.,.]] => 0
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => [.,[.,[.,[[.,.],[.,.]]]]] => 1
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [.,[.,[[[.,.],.],[.,.]]]] => 0
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[[.,.],.],[.,[[.,.],.]]] => 0
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],.]]] => [[[.,.],.],[[.,[.,.]],.]] => 0
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[[.,.],.],[[.,.],[.,.]]] => 0
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,.]]] => 0
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[[.,.],.],.],[[.,.],.]] => 0
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[.,.],[.,[.,.]]],.],.] => 0
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [[[[.,.],[.,.]],[.,.]],.] => 0
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 0
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 1
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 1
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 0
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 0
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 0
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 0
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 0
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 0
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 0
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 0
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 0
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 1
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 0
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 0
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 0
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 1
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 1
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 1
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 0
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 0
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 0
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => 0
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 0
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 1
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 0
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 0
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 0
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 0
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 0
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 0
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 1
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
>>> Load all 127 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 1
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 1
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 0
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 0
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 0
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 0
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 0
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 1
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 0
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 0
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 0
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 0
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 0
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 0
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [[[.,.],.],[[.,[[.,.],.]],.]] => 0
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 0
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [[[.,.],.],[[[.,.],.],[.,.]]] => 0
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 0
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[[.,.],.],.],[.,[[.,.],.]]] => 0
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => 0
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,.]]] => 0
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 0
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [[[[.,.],[.,[[.,.],.]]],.],.] => 0
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 0
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 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:A159768 counts binary trees avoiding this pattern.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
logarithmic height to pruning number
Description
Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].
Map
left rotate
Description
Return the result of left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let T be a binary tree such that the right child of the root of T is a node. Let A be the left child of the root of T, and let B and C be the left and right children of the right child of the root of T. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of T is the binary tree in which the right child of the root is C, whereas the left child of the root is a node whose left and right children are A and B.