Quote:

Find the number of ways of tiling a $\displaystyle 2 \times n$ rectangle with $\displaystyle 1 \times 2$ and $\displaystyle 2 \times 2$ tiles,

given that the edges of the tiles are parallel to those of the rectangle.

I have tried listing ways but that was only working through examples

(2 x 1 rectangle, 2 x 2 rectangle, 2 x 3 rectangle, so on),

but the number increases very quickly and starts getting quite confusing.

It also doesn't solve how many possibilities in terms of $\displaystyle n$.

How do i solve this, showing working where possible?