Identifier
Values
[1,0] => [.,.] => 0
[1,0,1,0] => [[.,.],.] => 0
[1,1,0,0] => [.,[.,.]] => 0
[1,0,1,0,1,0] => [[[.,.],.],.] => 0
[1,0,1,1,0,0] => [[.,.],[.,.]] => 0
[1,1,0,0,1,0] => [[.,[.,.]],.] => 0
[1,1,0,1,0,0] => [.,[[.,.],.]] => 0
[1,1,1,0,0,0] => [.,[.,[.,.]]] => 0
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 0
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 0
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 0
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 0
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 0
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 0
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 0
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 0
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => 1
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => 0
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 0
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => 0
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => 0
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => 0
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 0
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 0
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 0
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 0
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 0
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 0
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 0
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 0
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 1
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 0
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 0
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 0
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 0
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 0
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 0
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 0
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 0
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 0
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 0
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 0
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 0
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 1
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => 1
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => 1
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 0
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => 1
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => 0
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => 0
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 0
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 0
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 0
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => 1
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => 0
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 0
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => 0
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 1
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => 0
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 0
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => 0
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => 0
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => 0
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => 0
[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] => [[[[[.,.],.],.],.],[.,.]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 0
[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] => [[[.,.],.],[[.,.],[.,.]]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 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
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 0
[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] => [[.,.],[[.,.],[[.,.],.]]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 0
[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] => [[.,.],[[.,[.,.]],[.,.]]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 0
[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] => [[.,.],[.,[[.,.],[.,.]]]] => 0
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => 1
[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] => [.,[.,[[[.,.],.],[.,.]]]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,.]],[.,.]]]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => 0
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[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 0
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Description
The number of occurrences of the contiguous pattern [.,[[[.,.],.],.]] in a binary tree.
oeis:A005773 counts binary trees avoiding this pattern.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.