*****************************************************************************
*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
*                                                                           *
*    This information is distributed in the hope that it will be useful,    *
*    but WITHOUT ANY WARRANTY; without even the implied warranty of         *
*    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                   *
*****************************************************************************

-----------------------------------------------------------------------------
Statistic identifier: St000083

-----------------------------------------------------------------------------
Collection: Binary trees

-----------------------------------------------------------------------------
Description: The number of left oriented leafs of a binary tree except the first one.

In other other words, this is the sum of canopee vector of the tree.
The canopee of a non empty binary tree T with n internal nodes is the list l of 0 and 1 of length n-1 obtained by going along the leaves of T from left to right except the two extremal ones, writing 0 if the leaf is a right leaf and 1 if the leaf is a left leaf.

This is also the number of nodes having a right child. Indeed each of said right children will give exactly one left oriented leaf.

-----------------------------------------------------------------------------
References: 

-----------------------------------------------------------------------------
Code:
def statistic(bt):
    return sum(bt.canopee())

-----------------------------------------------------------------------------
Statistic values:

[.,[.,.]]                 => 1
[[.,.],.]                 => 0
[.,[.,[.,.]]]             => 2
[.,[[.,.],.]]             => 1
[[.,.],[.,.]]             => 1
[[.,[.,.]],.]             => 1
[[[.,.],.],.]             => 0
[.,[.,[.,[.,.]]]]         => 3
[.,[.,[[.,.],.]]]         => 2
[.,[[.,.],[.,.]]]         => 2
[.,[[.,[.,.]],.]]         => 2
[.,[[[.,.],.],.]]         => 1
[[.,.],[.,[.,.]]]         => 2
[[.,.],[[.,.],.]]         => 1
[[.,[.,.]],[.,.]]         => 2
[[[.,.],.],[.,.]]         => 1
[[.,[.,[.,.]]],.]         => 2
[[.,[[.,.],.]],.]         => 1
[[[.,.],[.,.]],.]         => 1
[[[.,[.,.]],.],.]         => 1
[[[[.,.],.],.],.]         => 0
[.,[.,[.,[.,[.,.]]]]]     => 4
[.,[.,[.,[[.,.],.]]]]     => 3
[.,[.,[[.,.],[.,.]]]]     => 3
[.,[.,[[.,[.,.]],.]]]     => 3
[.,[.,[[[.,.],.],.]]]     => 2
[.,[[.,.],[.,[.,.]]]]     => 3
[.,[[.,.],[[.,.],.]]]     => 2
[.,[[.,[.,.]],[.,.]]]     => 3
[.,[[[.,.],.],[.,.]]]     => 2
[.,[[.,[.,[.,.]]],.]]     => 3
[.,[[.,[[.,.],.]],.]]     => 2
[.,[[[.,.],[.,.]],.]]     => 2
[.,[[[.,[.,.]],.],.]]     => 2
[.,[[[[.,.],.],.],.]]     => 1
[[.,.],[.,[.,[.,.]]]]     => 3
[[.,.],[.,[[.,.],.]]]     => 2
[[.,.],[[.,.],[.,.]]]     => 2
[[.,.],[[.,[.,.]],.]]     => 2
[[.,.],[[[.,.],.],.]]     => 1
[[.,[.,.]],[.,[.,.]]]     => 3
[[.,[.,.]],[[.,.],.]]     => 2
[[[.,.],.],[.,[.,.]]]     => 2
[[[.,.],.],[[.,.],.]]     => 1
[[.,[.,[.,.]]],[.,.]]     => 3
[[.,[[.,.],.]],[.,.]]     => 2
[[[.,.],[.,.]],[.,.]]     => 2
[[[.,[.,.]],.],[.,.]]     => 2
[[[[.,.],.],.],[.,.]]     => 1
[[.,[.,[.,[.,.]]]],.]     => 3
[[.,[.,[[.,.],.]]],.]     => 2
[[.,[[.,.],[.,.]]],.]     => 2
[[.,[[.,[.,.]],.]],.]     => 2
[[.,[[[.,.],.],.]],.]     => 1
[[[.,.],[.,[.,.]]],.]     => 2
[[[.,.],[[.,.],.]],.]     => 1
[[[.,[.,.]],[.,.]],.]     => 2
[[[[.,.],.],[.,.]],.]     => 1
[[[.,[.,[.,.]]],.],.]     => 2
[[[.,[[.,.],.]],.],.]     => 1
[[[[.,.],[.,.]],.],.]     => 1
[[[[.,[.,.]],.],.],.]     => 1
[[[[[.,.],.],.],.],.]     => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => 5
[.,[.,[.,[.,[[.,.],.]]]]] => 4
[.,[.,[.,[[.,.],[.,.]]]]] => 4
[.,[.,[.,[[.,[.,.]],.]]]] => 4
[.,[.,[.,[[[.,.],.],.]]]] => 3
[.,[.,[[.,.],[.,[.,.]]]]] => 4
[.,[.,[[.,.],[[.,.],.]]]] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => 4
[.,[.,[[[.,.],.],[.,.]]]] => 3
[.,[.,[[.,[.,[.,.]]],.]]] => 4
[.,[.,[[.,[[.,.],.]],.]]] => 3
[.,[.,[[[.,.],[.,.]],.]]] => 3
[.,[.,[[[.,[.,.]],.],.]]] => 3
[.,[.,[[[[.,.],.],.],.]]] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => 4
[.,[[.,.],[.,[[.,.],.]]]] => 3
[.,[[.,.],[[.,.],[.,.]]]] => 3
[.,[[.,.],[[.,[.,.]],.]]] => 3
[.,[[.,.],[[[.,.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => 4
[.,[[.,[.,.]],[[.,.],.]]] => 3
[.,[[[.,.],.],[.,[.,.]]]] => 3
[.,[[[.,.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => 4
[.,[[.,[[.,.],.]],[.,.]]] => 3
[.,[[[.,.],[.,.]],[.,.]]] => 3
[.,[[[.,[.,.]],.],[.,.]]] => 3
[.,[[[[.,.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => 4
[.,[[.,[.,[[.,.],.]]],.]] => 3
[.,[[.,[[.,.],[.,.]]],.]] => 3
[.,[[.,[[.,[.,.]],.]],.]] => 3
[.,[[.,[[[.,.],.],.]],.]] => 2
[.,[[[.,.],[.,[.,.]]],.]] => 3
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 3
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 3
[.,[[[.,[[.,.],.]],.],.]] => 2
[.,[[[[.,.],[.,.]],.],.]] => 2
[.,[[[[.,[.,.]],.],.],.]] => 2
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 4
[[.,.],[.,[.,[[.,.],.]]]] => 3
[[.,.],[.,[[.,.],[.,.]]]] => 3
[[.,.],[.,[[.,[.,.]],.]]] => 3
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 3
[[.,.],[[.,.],[[.,.],.]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => 3
[[.,.],[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => 3
[[.,.],[[.,[[.,.],.]],.]] => 2
[[.,.],[[[.,.],[.,.]],.]] => 2
[[.,.],[[[.,[.,.]],.],.]] => 2
[[.,.],[[[[.,.],.],.],.]] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => 4
[[.,[.,.]],[.,[[.,.],.]]] => 3
[[.,[.,.]],[[.,.],[.,.]]] => 3
[[.,[.,.]],[[.,[.,.]],.]] => 3
[[.,[.,.]],[[[.,.],.],.]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => 3
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => 4
[[.,[.,[.,.]]],[[.,.],.]] => 3
[[.,[[.,.],.]],[.,[.,.]]] => 3
[[.,[[.,.],.]],[[.,.],.]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => 3
[[[.,.],[.,.]],[[.,.],.]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => 3
[[[.,[.,.]],.],[[.,.],.]] => 2
[[[[.,.],.],.],[.,[.,.]]] => 2
[[[[.,.],.],.],[[.,.],.]] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => 4
[[.,[.,[[.,.],.]]],[.,.]] => 3
[[.,[[.,.],[.,.]]],[.,.]] => 3
[[.,[[.,[.,.]],.]],[.,.]] => 3
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 3
[[[.,.],[[.,.],.]],[.,.]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => 3
[[[[.,.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => 3
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 2
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => 4
[[.,[.,[.,[[.,.],.]]]],.] => 3
[[.,[.,[[.,.],[.,.]]]],.] => 3
[[.,[.,[[.,[.,.]],.]]],.] => 3
[[.,[.,[[[.,.],.],.]]],.] => 2
[[.,[[.,.],[.,[.,.]]]],.] => 3
[[.,[[.,.],[[.,.],.]]],.] => 2
[[.,[[.,[.,.]],[.,.]]],.] => 3
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 3
[[.,[[.,[[.,.],.]],.]],.] => 2
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 2
[[.,[[[[.,.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,.]]]],.] => 3
[[[.,.],[.,[[.,.],.]]],.] => 2
[[[.,.],[[.,.],[.,.]]],.] => 2
[[[.,.],[[.,[.,.]],.]],.] => 2
[[[.,.],[[[.,.],.],.]],.] => 1
[[[.,[.,.]],[.,[.,.]]],.] => 3
[[[.,[.,.]],[[.,.],.]],.] => 2
[[[[.,.],.],[.,[.,.]]],.] => 2
[[[[.,.],.],[[.,.],.]],.] => 1
[[[.,[.,[.,.]]],[.,.]],.] => 3
[[[.,[[.,.],.]],[.,.]],.] => 2
[[[[.,.],[.,.]],[.,.]],.] => 2
[[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[.,.],.],.],[.,.]],.] => 1
[[[.,[.,[.,[.,.]]]],.],.] => 3
[[[.,[.,[[.,.],.]]],.],.] => 2
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 2
[[[.,[[[.,.],.],.]],.],.] => 1
[[[[.,.],[.,[.,.]]],.],.] => 2
[[[[.,.],[[.,.],.]],.],.] => 1
[[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[.,.],.],[.,.]],.],.] => 1
[[[[.,[.,[.,.]]],.],.],.] => 2
[[[[.,[[.,.],.]],.],.],.] => 1
[[[[[.,.],[.,.]],.],.],.] => 1
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 0

-----------------------------------------------------------------------------
Created: Jun 13, 2013 at 10:02 by Viviane Pons

-----------------------------------------------------------------------------
Last Updated: Oct 17, 2015 at 10:48 by Christian Stump