Identifier
Values
=>
Cc0010;cc-rep-0 Cc0021;cc-rep
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[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[],[[[],[[]]]],[],[]]=>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.
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 $y$.