According to wikipedia:
A tiling window manager is a window manager with an organization of the screen into mutually non-overlapping frames.
Mainly, this is done through List-based or Tree-based approaches.
In this method, windows are items in an ordered list. changing the position of windows in the list, rearrange windows. Different layouts could be applied. To illustrate this, consider a list of windows as [1, 2, 3, 4, 5, ...]. Then some layouts are depicted below.
in this method, windows are the leaves of a tree. and every internal node is a horizontal or vertical split that divides its own space among its children.
For simplicity let's have an exact kind of tree.
Case 4 will make trees like picture above to something like tree below.
If we ignore the order of children of each node, the number of possible trees with N windows is double (one with V and other with H as root) the Nth number in sequence A196545.