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Identifier

St001554: Binary trees ⟶ ℤ

Values

[.,.] => 1

[.,[.,.]] => 2

[[.,.],.] => 2

[.,[.,[.,.]]] => 3

[.,[[.,.],.]] => 3

[[.,.],[.,.]] => 2

[[.,[.,.]],.] => 3

[[[.,.],.],.] => 3

[.,[.,[.,[.,.]]]] => 4

[.,[.,[[.,.],.]]] => 4

[.,[[.,.],[.,.]]] => 3

[.,[[.,[.,.]],.]] => 4

[.,[[[.,.],.],.]] => 4

[[.,.],[.,[.,.]]] => 3

[[.,.],[[.,.],.]] => 3

[[.,[.,.]],[.,.]] => 3

[[[.,.],.],[.,.]] => 3

[[.,[.,[.,.]]],.] => 4

[[.,[[.,.],.]],.] => 4

[[[.,.],[.,.]],.] => 3

[[[.,[.,.]],.],.] => 4

[[[[.,.],.],.],.] => 4

[.,[.,[.,[.,[.,.]]]]] => 5

[.,[.,[.,[[.,.],.]]]] => 5

[.,[.,[[.,.],[.,.]]]] => 4

[.,[.,[[.,[.,.]],.]]] => 5

[.,[.,[[[.,.],.],.]]] => 5

[.,[[.,.],[.,[.,.]]]] => 4

[.,[[.,.],[[.,.],.]]] => 4

[.,[[.,[.,.]],[.,.]]] => 4

[.,[[[.,.],.],[.,.]]] => 4

[.,[[.,[.,[.,.]]],.]] => 5

[.,[[.,[[.,.],.]],.]] => 5

[.,[[[.,.],[.,.]],.]] => 4

[.,[[[.,[.,.]],.],.]] => 5

[.,[[[[.,.],.],.],.]] => 5

[[.,.],[.,[.,[.,.]]]] => 4

[[.,.],[.,[[.,.],.]]] => 4

[[.,.],[[.,.],[.,.]]] => 3

[[.,.],[[.,[.,.]],.]] => 4

[[.,.],[[[.,.],.],.]] => 4

[[.,[.,.]],[.,[.,.]]] => 3

[[.,[.,.]],[[.,.],.]] => 4

[[[.,.],.],[.,[.,.]]] => 4

[[[.,.],.],[[.,.],.]] => 3

[[.,[.,[.,.]]],[.,.]] => 4

[[.,[[.,.],.]],[.,.]] => 4

[[[.,.],[.,.]],[.,.]] => 3

[[[.,[.,.]],.],[.,.]] => 4

[[[[.,.],.],.],[.,.]] => 4

[[.,[.,[.,[.,.]]]],.] => 5

[[.,[.,[[.,.],.]]],.] => 5

[[.,[[.,.],[.,.]]],.] => 4

[[.,[[.,[.,.]],.]],.] => 5

[[.,[[[.,.],.],.]],.] => 5

[[[.,.],[.,[.,.]]],.] => 4

[[[.,.],[[.,.],.]],.] => 4

[[[.,[.,.]],[.,.]],.] => 4

[[[[.,.],.],[.,.]],.] => 4

[[[.,[.,[.,.]]],.],.] => 5

[[[.,[[.,.],.]],.],.] => 5

[[[[.,.],[.,.]],.],.] => 4

[[[[.,[.,.]],.],.],.] => 5

[[[[[.,.],.],.],.],.] => 5

[.,[.,[.,[.,[.,[.,.]]]]]] => 6

[.,[.,[.,[.,[[.,.],.]]]]] => 6

[.,[.,[.,[[.,.],[.,.]]]]] => 5

[.,[.,[.,[[.,[.,.]],.]]]] => 6

[.,[.,[.,[[[.,.],.],.]]]] => 6

[.,[.,[[.,.],[.,[.,.]]]]] => 5

[.,[.,[[.,.],[[.,.],.]]]] => 5

[.,[.,[[.,[.,.]],[.,.]]]] => 5

[.,[.,[[[.,.],.],[.,.]]]] => 5

[.,[.,[[.,[.,[.,.]]],.]]] => 6

[.,[.,[[.,[[.,.],.]],.]]] => 6

[.,[.,[[[.,.],[.,.]],.]]] => 5

[.,[.,[[[.,[.,.]],.],.]]] => 6

[.,[.,[[[[.,.],.],.],.]]] => 6

[.,[[.,.],[.,[.,[.,.]]]]] => 5

[.,[[.,.],[.,[[.,.],.]]]] => 5

[.,[[.,.],[[.,.],[.,.]]]] => 4

[.,[[.,.],[[.,[.,.]],.]]] => 5

[.,[[.,.],[[[.,.],.],.]]] => 5

[.,[[.,[.,.]],[.,[.,.]]]] => 4

[.,[[.,[.,.]],[[.,.],.]]] => 5

[.,[[[.,.],.],[.,[.,.]]]] => 5

[.,[[[.,.],.],[[.,.],.]]] => 4

[.,[[.,[.,[.,.]]],[.,.]]] => 5

[.,[[.,[[.,.],.]],[.,.]]] => 5

[.,[[[.,.],[.,.]],[.,.]]] => 4

[.,[[[.,[.,.]],.],[.,.]]] => 5

[.,[[[[.,.],.],.],[.,.]]] => 5

[.,[[.,[.,[.,[.,.]]]],.]] => 6

[.,[[.,[.,[[.,.],.]]],.]] => 6

[.,[[.,[[.,.],[.,.]]],.]] => 5

[.,[[.,[[.,[.,.]],.]],.]] => 6

[.,[[.,[[[.,.],.],.]],.]] => 6

[.,[[[.,.],[.,[.,.]]],.]] => 5

[.,[[[.,.],[[.,.],.]],.]] => 5

[.,[[[.,[.,.]],[.,.]],.]] => 5

[.,[[[[.,.],.],[.,.]],.]] => 5

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Description

The number of distinct nonempty subtrees of a binary tree.

References

[1] The number of unlabeled binary trees that contain n distinct subtrees, where a subtree means take any node and everything below that node. OEIS:A254789

Code

def statistic(B):
    return len(set([T for T in B.subtrees()]))

Created

Jun 05, 2020 at 14:17 by Martin Rubey

Updated

Jun 05, 2020 at 14:17 by Martin Rubey