MathNet 2008-part-02 — 165 problems (EN–VI) Question 44

Let $n \geq 2$ be an integer. We colour all the cells of an $n \times n$ board red or blue so that every $2 \times 2$ square contained in the board has exactly two red cells and two blue cells.
How many colourings are possible?

NOTE: two colourings that are obtained from one another by a rotation or a symmetry of the board are considered distinct.