Identifier
-
Mp00010:
Binary trees
—to ordered tree: left child = left brother⟶
Ordered trees
St000522: Ordered trees ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0021;cc-rep
[.,.]=>[[]]=>1
[.,[.,.]]=>[[[]]]=>1
[[.,.],.]=>[[],[]]=>1
[.,[.,[.,.]]]=>[[[[]]]]=>1
[.,[[.,.],.]]=>[[[],[]]]=>1
[[.,.],[.,.]]=>[[],[[]]]=>2
[[.,[.,.]],.]=>[[[]],[]]=>2
[[[.,.],.],.]=>[[],[],[]]=>1
[.,[.,[.,[.,.]]]]=>[[[[[]]]]]=>1
[.,[.,[[.,.],.]]]=>[[[[],[]]]]=>1
[.,[[.,.],[.,.]]]=>[[[],[[]]]]=>2
[.,[[.,[.,.]],.]]=>[[[[]],[]]]=>2
[.,[[[.,.],.],.]]=>[[[],[],[]]]=>1
[[.,.],[.,[.,.]]]=>[[],[[[]]]]=>2
[[.,.],[[.,.],.]]=>[[],[[],[]]]=>2
[[.,[.,.]],[.,.]]=>[[[]],[[]]]=>2
[[[.,.],.],[.,.]]=>[[],[],[[]]]=>2
[[.,[.,[.,.]]],.]=>[[[[]]],[]]=>2
[[.,[[.,.],.]],.]=>[[[],[]],[]]=>2
[[[.,.],[.,.]],.]=>[[],[[]],[]]=>2
[[[.,[.,.]],.],.]=>[[[]],[],[]]=>2
[[[[.,.],.],.],.]=>[[],[],[],[]]=>1
[.,[.,[.,[.,[.,.]]]]]=>[[[[[[]]]]]]=>1
[.,[.,[.,[[.,.],.]]]]=>[[[[[],[]]]]]=>1
[.,[.,[[.,.],[.,.]]]]=>[[[[],[[]]]]]=>2
[.,[.,[[.,[.,.]],.]]]=>[[[[[]],[]]]]=>2
[.,[.,[[[.,.],.],.]]]=>[[[[],[],[]]]]=>1
[.,[[.,.],[.,[.,.]]]]=>[[[],[[[]]]]]=>2
[.,[[.,.],[[.,.],.]]]=>[[[],[[],[]]]]=>2
[.,[[.,[.,.]],[.,.]]]=>[[[[]],[[]]]]=>2
[.,[[[.,.],.],[.,.]]]=>[[[],[],[[]]]]=>2
[.,[[.,[.,[.,.]]],.]]=>[[[[[]]],[]]]=>2
[.,[[.,[[.,.],.]],.]]=>[[[[],[]],[]]]=>2
[.,[[[.,.],[.,.]],.]]=>[[[],[[]],[]]]=>2
[.,[[[.,[.,.]],.],.]]=>[[[[]],[],[]]]=>2
[.,[[[[.,.],.],.],.]]=>[[[],[],[],[]]]=>1
[[.,.],[.,[.,[.,.]]]]=>[[],[[[[]]]]]=>2
[[.,.],[.,[[.,.],.]]]=>[[],[[[],[]]]]=>2
[[.,.],[[.,.],[.,.]]]=>[[],[[],[[]]]]=>3
[[.,.],[[.,[.,.]],.]]=>[[],[[[]],[]]]=>3
[[.,.],[[[.,.],.],.]]=>[[],[[],[],[]]]=>2
[[.,[.,.]],[.,[.,.]]]=>[[[]],[[[]]]]=>2
[[.,[.,.]],[[.,.],.]]=>[[[]],[[],[]]]=>2
[[[.,.],.],[.,[.,.]]]=>[[],[],[[[]]]]=>2
[[[.,.],.],[[.,.],.]]=>[[],[],[[],[]]]=>2
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[[.,[[.,.],.]],[.,.]]=>[[[],[]],[[]]]=>2
[[[.,.],[.,.]],[.,.]]=>[[],[[]],[[]]]=>3
[[[.,[.,.]],.],[.,.]]=>[[[]],[],[[]]]=>3
[[[[.,.],.],.],[.,.]]=>[[],[],[],[[]]]=>2
[[.,[.,[.,[.,.]]]],.]=>[[[[[]]]],[]]=>2
[[.,[.,[[.,.],.]]],.]=>[[[[],[]]],[]]=>2
[[.,[[.,.],[.,.]]],.]=>[[[],[[]]],[]]=>3
[[.,[[.,[.,.]],.]],.]=>[[[[]],[]],[]]=>3
[[.,[[[.,.],.],.]],.]=>[[[],[],[]],[]]=>2
[[[.,.],[.,[.,.]]],.]=>[[],[[[]]],[]]=>2
[[[.,.],[[.,.],.]],.]=>[[],[[],[]],[]]=>2
[[[.,[.,.]],[.,.]],.]=>[[[]],[[]],[]]=>3
[[[[.,.],.],[.,.]],.]=>[[],[],[[]],[]]=>2
[[[.,[.,[.,.]]],.],.]=>[[[[]]],[],[]]=>2
[[[.,[[.,.],.]],.],.]=>[[[],[]],[],[]]=>2
[[[[.,.],[.,.]],.],.]=>[[],[[]],[],[]]=>2
[[[[.,[.,.]],.],.],.]=>[[[]],[],[],[]]=>2
[[[[[.,.],.],.],.],.]=>[[],[],[],[],[]]=>1
[.,[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[[]]]]]]]=>1
[.,[.,[.,[.,[[.,.],.]]]]]=>[[[[[[],[]]]]]]=>1
[.,[.,[.,[[.,.],[.,.]]]]]=>[[[[[],[[]]]]]]=>2
[.,[.,[.,[[.,[.,.]],.]]]]=>[[[[[[]],[]]]]]=>2
[.,[.,[.,[[[.,.],.],.]]]]=>[[[[[],[],[]]]]]=>1
[.,[.,[[.,.],[.,[.,.]]]]]=>[[[[],[[[]]]]]]=>2
[.,[.,[[.,.],[[.,.],.]]]]=>[[[[],[[],[]]]]]=>2
[.,[.,[[.,[.,.]],[.,.]]]]=>[[[[[]],[[]]]]]=>2
[.,[.,[[[.,.],.],[.,.]]]]=>[[[[],[],[[]]]]]=>2
[.,[.,[[.,[.,[.,.]]],.]]]=>[[[[[[]]],[]]]]=>2
[.,[.,[[.,[[.,.],.]],.]]]=>[[[[[],[]],[]]]]=>2
[.,[.,[[[.,.],[.,.]],.]]]=>[[[[],[[]],[]]]]=>2
[.,[.,[[[.,[.,.]],.],.]]]=>[[[[[]],[],[]]]]=>2
[.,[.,[[[[.,.],.],.],.]]]=>[[[[],[],[],[]]]]=>1
[.,[[.,.],[.,[.,[.,.]]]]]=>[[[],[[[[]]]]]]=>2
[.,[[.,.],[.,[[.,.],.]]]]=>[[[],[[[],[]]]]]=>2
[.,[[.,.],[[.,.],[.,.]]]]=>[[[],[[],[[]]]]]=>3
[.,[[.,.],[[.,[.,.]],.]]]=>[[[],[[[]],[]]]]=>3
[.,[[.,.],[[[.,.],.],.]]]=>[[[],[[],[],[]]]]=>2
[.,[[.,[.,.]],[.,[.,.]]]]=>[[[[]],[[[]]]]]=>2
[.,[[.,[.,.]],[[.,.],.]]]=>[[[[]],[[],[]]]]=>2
[.,[[[.,.],.],[.,[.,.]]]]=>[[[],[],[[[]]]]]=>2
[.,[[[.,.],.],[[.,.],.]]]=>[[[],[],[[],[]]]]=>2
[.,[[.,[.,[.,.]]],[.,.]]]=>[[[[[]]],[[]]]]=>2
[.,[[.,[[.,.],.]],[.,.]]]=>[[[[],[]],[[]]]]=>2
[.,[[[.,.],[.,.]],[.,.]]]=>[[[],[[]],[[]]]]=>3
[.,[[[.,[.,.]],.],[.,.]]]=>[[[[]],[],[[]]]]=>3
[.,[[[[.,.],.],.],[.,.]]]=>[[[],[],[],[[]]]]=>2
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[.,[[.,[[.,.],[.,.]]],.]]=>[[[[],[[]]],[]]]=>3
[.,[[.,[[.,[.,.]],.]],.]]=>[[[[[]],[]],[]]]=>3
[.,[[.,[[[.,.],.],.]],.]]=>[[[[],[],[]],[]]]=>2
[.,[[[.,.],[.,[.,.]]],.]]=>[[[],[[[]]],[]]]=>2
[.,[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]],[]]]=>2
[.,[[[.,[.,.]],[.,.]],.]]=>[[[[]],[[]],[]]]=>3
[.,[[[[.,.],.],[.,.]],.]]=>[[[],[],[[]],[]]]=>2
[.,[[[.,[.,[.,.]]],.],.]]=>[[[[[]]],[],[]]]=>2
[.,[[[.,[[.,.],.]],.],.]]=>[[[[],[]],[],[]]]=>2
[.,[[[[.,.],[.,.]],.],.]]=>[[[],[[]],[],[]]]=>2
[.,[[[[.,[.,.]],.],.],.]]=>[[[[]],[],[],[]]]=>2
[.,[[[[[.,.],.],.],.],.]]=>[[[],[],[],[],[]]]=>1
[[.,.],[.,[.,[.,[.,.]]]]]=>[[],[[[[[]]]]]]=>2
[[.,.],[.,[.,[[.,.],.]]]]=>[[],[[[[],[]]]]]=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[[],[[[],[[]]]]]=>3
[[.,.],[.,[[.,[.,.]],.]]]=>[[],[[[[]],[]]]]=>3
[[.,.],[.,[[[.,.],.],.]]]=>[[],[[[],[],[]]]]=>2
[[.,.],[[.,.],[.,[.,.]]]]=>[[],[[],[[[]]]]]=>3
[[.,.],[[.,.],[[.,.],.]]]=>[[],[[],[[],[]]]]=>3
[[.,.],[[.,[.,.]],[.,.]]]=>[[],[[[]],[[]]]]=>3
[[.,.],[[[.,.],.],[.,.]]]=>[[],[[],[],[[]]]]=>3
[[.,.],[[.,[.,[.,.]]],.]]=>[[],[[[[]]],[]]]=>3
[[.,.],[[.,[[.,.],.]],.]]=>[[],[[[],[]],[]]]=>3
[[.,.],[[[.,.],[.,.]],.]]=>[[],[[],[[]],[]]]=>3
[[.,.],[[[.,[.,.]],.],.]]=>[[],[[[]],[],[]]]=>3
[[.,.],[[[[.,.],.],.],.]]=>[[],[[],[],[],[]]]=>2
[[.,[.,.]],[.,[.,[.,.]]]]=>[[[]],[[[[]]]]]=>2
[[.,[.,.]],[.,[[.,.],.]]]=>[[[]],[[[],[]]]]=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[[[]],[[],[[]]]]=>3
[[.,[.,.]],[[.,[.,.]],.]]=>[[[]],[[[]],[]]]=>3
[[.,[.,.]],[[[.,.],.],.]]=>[[[]],[[],[],[]]]=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[[],[],[[[[]]]]]=>2
[[[.,.],.],[.,[[.,.],.]]]=>[[],[],[[[],[]]]]=>2
[[[.,.],.],[[.,.],[.,.]]]=>[[],[],[[],[[]]]]=>3
[[[.,.],.],[[.,[.,.]],.]]=>[[],[],[[[]],[]]]=>3
[[[.,.],.],[[[.,.],.],.]]=>[[],[],[[],[],[]]]=>2
[[.,[.,[.,.]]],[.,[.,.]]]=>[[[[]]],[[[]]]]=>2
[[.,[.,[.,.]]],[[.,.],.]]=>[[[[]]],[[],[]]]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[[[],[]],[[[]]]]=>2
[[.,[[.,.],.]],[[.,.],.]]=>[[[],[]],[[],[]]]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[[],[[]],[[[]]]]=>3
[[[.,.],[.,.]],[[.,.],.]]=>[[],[[]],[[],[]]]=>3
[[[.,[.,.]],.],[.,[.,.]]]=>[[[]],[],[[[]]]]=>3
[[[.,[.,.]],.],[[.,.],.]]=>[[[]],[],[[],[]]]=>3
[[[[.,.],.],.],[.,[.,.]]]=>[[],[],[],[[[]]]]=>2
[[[[.,.],.],.],[[.,.],.]]=>[[],[],[],[[],[]]]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>[[[[[]]]],[[]]]=>2
[[.,[.,[[.,.],.]]],[.,.]]=>[[[[],[]]],[[]]]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>[[[],[[]]],[[]]]=>3
[[.,[[.,[.,.]],.]],[.,.]]=>[[[[]],[]],[[]]]=>3
[[.,[[[.,.],.],.]],[.,.]]=>[[[],[],[]],[[]]]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>[[],[[[]]],[[]]]=>3
[[[.,.],[[.,.],.]],[.,.]]=>[[],[[],[]],[[]]]=>3
[[[.,[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]]]=>3
[[[[.,.],.],[.,.]],[.,.]]=>[[],[],[[]],[[]]]=>3
[[[.,[.,[.,.]]],.],[.,.]]=>[[[[]]],[],[[]]]=>3
[[[.,[[.,.],.]],.],[.,.]]=>[[[],[]],[],[[]]]=>3
[[[[.,.],[.,.]],.],[.,.]]=>[[],[[]],[],[[]]]=>3
[[[[.,[.,.]],.],.],[.,.]]=>[[[]],[],[],[[]]]=>3
[[[[[.,.],.],.],.],[.,.]]=>[[],[],[],[],[[]]]=>2
[[.,[.,[.,[.,[.,.]]]]],.]=>[[[[[[]]]]],[]]=>2
[[.,[.,[.,[[.,.],.]]]],.]=>[[[[[],[]]]],[]]=>2
[[.,[.,[[.,.],[.,.]]]],.]=>[[[[],[[]]]],[]]=>3
[[.,[.,[[.,[.,.]],.]]],.]=>[[[[[]],[]]],[]]=>3
[[.,[.,[[[.,.],.],.]]],.]=>[[[[],[],[]]],[]]=>2
[[.,[[.,.],[.,[.,.]]]],.]=>[[[],[[[]]]],[]]=>3
[[.,[[.,.],[[.,.],.]]],.]=>[[[],[[],[]]],[]]=>3
[[.,[[.,[.,.]],[.,.]]],.]=>[[[[]],[[]]],[]]=>3
[[.,[[[.,.],.],[.,.]]],.]=>[[[],[],[[]]],[]]=>3
[[.,[[.,[.,[.,.]]],.]],.]=>[[[[[]]],[]],[]]=>3
[[.,[[.,[[.,.],.]],.]],.]=>[[[[],[]],[]],[]]=>3
[[.,[[[.,.],[.,.]],.]],.]=>[[[],[[]],[]],[]]=>3
[[.,[[[.,[.,.]],.],.]],.]=>[[[[]],[],[]],[]]=>3
[[.,[[[[.,.],.],.],.]],.]=>[[[],[],[],[]],[]]=>2
[[[.,.],[.,[.,[.,.]]]],.]=>[[],[[[[]]]],[]]=>2
[[[.,.],[.,[[.,.],.]]],.]=>[[],[[[],[]]],[]]=>2
[[[.,.],[[.,.],[.,.]]],.]=>[[],[[],[[]]],[]]=>3
[[[.,.],[[.,[.,.]],.]],.]=>[[],[[[]],[]],[]]=>3
[[[.,.],[[[.,.],.],.]],.]=>[[],[[],[],[]],[]]=>2
[[[.,[.,.]],[.,[.,.]]],.]=>[[[]],[[[]]],[]]=>3
[[[.,[.,.]],[[.,.],.]],.]=>[[[]],[[],[]],[]]=>3
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[[[[.,.],.],[[.,.],.]],.]=>[[],[],[[],[]],[]]=>2
[[[.,[.,[.,.]]],[.,.]],.]=>[[[[]]],[[]],[]]=>3
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[[[.,[.,[.,[.,.]]]],.],.]=>[[[[[]]]],[],[]]=>2
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[[[[.,.],[.,[.,.]]],.],.]=>[[],[[[]]],[],[]]=>2
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[[[[.,[.,[.,.]]],.],.],.]=>[[[[]]],[],[],[]]=>2
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[[[[[[.,.],.],.],.],.],.]=>[[],[],[],[],[],[]]=>1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[[]]]]]]]]=>1
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[[],[]]]]]]]=>1
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[],[[]]]]]]]=>2
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[[[]],[]]]]]]=>2
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[[],[],[]]]]]]=>1
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[[[],[[[]]]]]]]=>2
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[[[[],[[],[]]]]]]=>2
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[[]],[[]]]]]]=>2
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[],[],[[]]]]]]=>2
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[[[[]]],[]]]]]=>2
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[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[[[]],[[[]]]]]]=>2
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[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[[[[],[[]]],[]]]]=>3
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[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[[[[],[],[]],[]]]]=>2
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[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[[[],[[],[]],[]]]]=>2
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[[[[]],[[]],[]]]]=>3
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[[[],[],[[]],[]]]]=>2
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[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[[],[[]],[],[]]]]=>2
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[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[],[[[[],[]]]]]]=>2
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[[[],[[]]]]]]=>3
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[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[[[]],[[]],[[]]]]=>3
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[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[[[[]]],[],[[]]]]=>3
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[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[],[[[[]],[],[]]],[]]=>3
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[],[[[],[],[],[]]],[]]=>2
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[],[[],[[[[]]]]],[]]=>3
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[[],[[],[[[],[]]]],[]]=>3
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[],[[],[[],[[]]]],[]]=>4
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[],[[],[[[]],[]]],[]]=>4
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[],[[],[[],[],[]]],[]]=>3
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[],[[[]],[[[]]]],[]]=>3
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[],[[[]],[[],[]]],[]]=>3
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[],[[],[],[[[]]]],[]]=>3
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[],[[],[],[[],[]]],[]]=>3
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[],[[[[]]],[[]]],[]]=>3
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[],[[[],[]],[[]]],[]]=>3
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[],[[],[[]],[[]]],[]]=>4
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[],[[[]],[],[[]]],[]]=>4
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[],[[],[],[],[[]]],[]]=>3
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[],[[[[[]]]],[]],[]]=>3
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[],[[[[],[]]],[]],[]]=>3
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[],[[[],[[]]],[]],[]]=>4
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[],[[[[]],[]],[]],[]]=>4
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[],[[[],[],[]],[]],[]]=>3
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[],[[],[[[]]],[]],[]]=>3
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[],[[],[[],[]],[]],[]]=>3
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[],[[[]],[[]],[]],[]]=>4
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[],[[],[],[[]],[]],[]]=>3
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[],[[[[]]],[],[]],[]]=>3
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[],[[[],[]],[],[]],[]]=>3
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[],[[],[[]],[],[]],[]]=>3
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[],[[[]],[],[],[]],[]]=>3
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[],[[],[],[],[],[]],[]]=>2
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[]],[[[[[]]]]],[]]=>3
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[]],[[[[],[]]]],[]]=>3
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[]],[[[],[[]]]],[]]=>4
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[]],[[[[]],[]]],[]]=>4
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[]],[[[],[],[]]],[]]=>3
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[]],[[],[[[]]]],[]]=>4
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[]],[[],[[],[]]],[]]=>4
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[]],[[[]],[[]]],[]]=>4
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[]],[[],[],[[]]],[]]=>4
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[]],[[[[]]],[]],[]]=>4
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[]],[[[],[]],[]],[]]=>4
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[]],[[],[[]],[]],[]]=>4
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[]],[[[]],[],[]],[]]=>4
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[]],[[],[],[],[]],[]]=>3
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[],[],[[[[[]]]]],[]]=>2
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[],[],[[[[],[]]]],[]]=>2
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[],[],[[[],[[]]]],[]]=>3
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[],[],[[[[]],[]]],[]]=>3
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[],[],[[[],[],[]]],[]]=>2
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[],[],[[],[[[]]]],[]]=>3
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[],[],[[],[[],[]]],[]]=>3
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[],[],[[[]],[[]]],[]]=>3
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[],[],[[],[],[[]]],[]]=>3
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[],[],[[[[]]],[]],[]]=>3
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[],[],[[[],[]],[]],[]]=>3
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[],[],[[],[[]],[]],[]]=>3
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[],[],[[[]],[],[]],[]]=>3
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[],[],[[],[],[],[]],[]]=>2
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[],[[]],[[[[]]]],[]]=>3
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[],[[]],[[[],[]]],[]]=>3
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[],[[]],[[],[[]]],[]]=>4
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[],[[]],[[[]],[]],[]]=>4
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[],[[]],[[],[],[]],[]]=>3
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[]],[],[[[[]]]],[]]=>3
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[]],[],[[[],[]]],[]]=>3
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[]],[],[[],[[]]],[]]=>4
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[]],[],[[[]],[]],[]]=>4
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[]],[],[[],[],[]],[]]=>3
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[],[],[],[[[[]]]],[]]=>2
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[],[],[],[[[],[]]],[]]=>2
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[],[],[],[[],[[]]],[]]=>3
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[],[],[],[[[]],[]],[]]=>3
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[],[],[],[[],[],[]],[]]=>2
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[],[[[]]],[[[]]],[]]=>3
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[],[[[]]],[[],[]],[]]=>3
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[],[[],[]],[[[]]],[]]=>3
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[],[[],[]],[[],[]],[]]=>3
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[]],[[]],[[[]]],[]]=>4
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[]],[[]],[[],[]],[]]=>4
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[],[],[[]],[[[]]],[]]=>3
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[],[],[[]],[[],[]],[]]=>3
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[],[[]],[],[[[]]],[]]=>3
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[],[[]],[],[[],[]],[]]=>3
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[]],[],[],[[[]]],[]]=>3
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[]],[],[],[[],[]],[]]=>3
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[],[],[],[],[[[]]],[]]=>2
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[],[],[],[],[[],[]],[]]=>2
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[],[[[[]]]],[[]],[]]=>3
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[],[[[],[]]],[[]],[]]=>3
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[],[[],[[]]],[[]],[]]=>4
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[],[[[]],[]],[[]],[]]=>4
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[],[[],[],[]],[[]],[]]=>3
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[]],[[[]]],[[]],[]]=>4
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[]],[[],[]],[[]],[]]=>4
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[],[],[[[]]],[[]],[]]=>3
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[],[],[[],[]],[[]],[]]=>3
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[],[[]],[[]],[[]],[]]=>4
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[]],[],[[]],[[]],[]]=>4
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[],[],[],[[]],[[]],[]]=>3
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[],[[[]]],[],[[]],[]]=>3
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[],[[],[]],[],[[]],[]]=>3
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[]],[[]],[],[[]],[]]=>4
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[],[],[[]],[],[[]],[]]=>3
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[]]],[],[],[[]],[]]=>3
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[],[]],[],[],[[]],[]]=>3
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[],[[]],[],[],[[]],[]]=>3
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[]],[],[],[],[[]],[]]=>3
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[[]],[]]=>2
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[],[[[[[]]]]],[],[]]=>2
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[],[[[[],[]]]],[],[]]=>2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[],[[[],[[]]]],[],[]]=>3
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[],[[[[]],[]]],[],[]]=>3
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[],[[[],[],[]]],[],[]]=>2
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[],[[],[[[]]]],[],[]]=>3
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[],[[],[[],[]]],[],[]]=>3
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[],[[[]],[[]]],[],[]]=>3
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[],[[],[],[[]]],[],[]]=>3
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[],[[[[]]],[]],[],[]]=>3
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[],[[[],[]],[]],[],[]]=>3
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[],[[],[[]],[]],[],[]]=>3
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[],[[[]],[],[]],[],[]]=>3
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[],[[],[],[],[]],[],[]]=>2
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[]],[[[[]]]],[],[]]=>3
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[]],[[[],[]]],[],[]]=>3
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[]],[[],[[]]],[],[]]=>4
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[]],[[[]],[]],[],[]]=>4
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[]],[[],[],[]],[],[]]=>3
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[],[],[[[[]]]],[],[]]=>2
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[],[],[[[],[]]],[],[]]=>2
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[],[],[[],[[]]],[],[]]=>3
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[],[],[[[]],[]],[],[]]=>3
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[],[],[[],[],[]],[],[]]=>2
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[],[[]],[[[]]],[],[]]=>3
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[],[[]],[[],[]],[],[]]=>3
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[]],[],[[[]]],[],[]]=>3
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[]],[],[[],[]],[],[]]=>3
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[],[],[],[[[]]],[],[]]=>2
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[],[],[],[[],[]],[],[]]=>2
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[],[[[]]],[[]],[],[]]=>3
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[],[[],[]],[[]],[],[]]=>3
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[]],[[]],[[]],[],[]]=>4
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[],[],[[]],[[]],[],[]]=>3
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[]]],[],[[]],[],[]]=>3
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[],[]],[],[[]],[],[]]=>3
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[],[[]],[],[[]],[],[]]=>3
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[]],[],[],[[]],[],[]]=>3
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[[]],[],[]]=>2
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[],[[[[]]]],[],[],[]]=>2
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[],[[[],[]]],[],[],[]]=>2
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[],[[],[[]]],[],[],[]]=>3
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[],[[[]],[]],[],[],[]]=>3
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[],[[],[],[]],[],[],[]]=>2
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[]],[[[]]],[],[],[]]=>3
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[]],[[],[]],[],[],[]]=>3
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[],[],[[[]]],[],[],[]]=>2
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>2
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>3
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]=>3
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]=>2
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>2
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>2
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>3
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]=>2
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>2
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]=>2
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]=>2
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]=>2
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]=>1
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Description
The number of 1-protected nodes of a rooted tree.
This is the number of nodes with minimal distance one to a leaf.
This is the number of nodes with minimal distance one to a leaf.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
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