P162: Enumeration of all triconnected plane triangulations with exactly $n$ vertices and $r$ leaves

P162: Enumeration of all triconnected plane triangulations with exactly $n$ vertices and $r$ leaves
Input:
An integer $n$.
Output:
All triconnected plane triangulations with exactly $n$ vertices and $r$ leaves.
Complexity:
$O(r^n)$ time per triangulation and $O(n)$ space.
Comment:
Reference:
[Nakano2001] (Bibtex)