# Display count of leaves(depth) at each level in tree

I am drawing a tree like given below. The MWE for it is below:

\documentclass[]{article}
\usepackage{forest}
\title{}
\author{}
\begin{document}
\date{}
\begin{forest}
[n
[n-1
[n-2[$\vdots$]][n-2[$\vdots$]]]
[n-1
[n-2[$\vdots$]][n-2[$\vdots$]]]]
\end{forest}
\end{document}


I wish to write the count of number of nodes at each level of the tree. For example, adjacent to n, I wish to write 1. In the next level, 2 and so on. Since I am using forest package,

[n\hspace{1cm}1]


doesn't seem to help. Any simple ideas on how to do this?

### Edit 1:

I found a related question which is not working for me.

A simple robust way would be to name one of the nodes in each level and use the y coordinate of that node (making use of the calc tikzlibrary) to get the correct height for each label. Counting the number of nodes can be done progrmatically - in your case the formula is clearly 2^n (use pgfs pow):

\documentclass[]{article}
\usepackage{forest}
\usetikzlibrary{calc} % let
\newcommand\leftsep{3} % How far left of center line of forest labels appear (cm)
\newcounter{levelcount} % Stores current level in tree
\newcommand\countnodes[1]{% Command to add label at height of node #1
\draw let \p{L} = (#1) in (-\leftsep,\y{L}) node {\pgfmathparse{int(pow(2,\value{levelcount}))}\pgfmathresult};
\stepcounter{levelcount} % Step counter for next level
}
\begin{document}
\begin{forest}
[n, name=root % Name root
[n-1, name=level1 % Name a node in level 1
[n-2, name=level2 [$\vdots$]][n-2[$\vdots$]]] % Name a node in level 2
[n-1
[n-2[$\vdots$]][n-2[$\vdots$]]]]
{% Node counting - these must be in order
\countnodes{root}
\countnodes{level1}
\countnodes{level2}
}
\end{forest}
\end{document}


Output:

• After the vdots, I would like to write 2 raised to k, for the k-th level of nodes. I assume this cannot be done using this approach. – GermanShepherd Feb 25 at 10:48
• Sure, just name your vdots node e.g. mydots and add a command like \draw let \p{L} = (mydots) in (-\leftsep,\y{L}) node {$2^k$}; in the same group ({..}) as the \countnodes commands. (If you want it below the vdots, use e.g. \y{L}-1 instead of \y{L}.) – Pippip19 Feb 25 at 10:59