Find the number of ways of tiling a "2 xn" rectangle with "1 x 2" and "2 x 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, 2 x 4 and so on, but the number increases very quickly and starts getting quite confusing. It also doesn't solve how many possibilities fornassumably in terms ofn. How do i solve this showing working where possible??