P156: Enumeration of all based floorplans with exactly $n$ faces

P156: Enumeration of all based floorplans with exactly $n$ faces
Input:
An integer $n$.
Output:
All based floorplans with exactly $n$ faces.
Complexity:
$O(1)$ time per solution with $O(n)$ space.
Comment:
A planar graph is called a \textit{floorplan} if every face is a rectangle. A \textit{based floorplan} is a floorplan with one designated base line segment on the outer face.
Reference:
[Nakano2001a] (Bibtex)