# $$n \times n$$ square paint

A board of $$n cm \times n cm$$ is divided in $$n^2$$ little squares of $$1cm \times 1 cm$$. If each square can be painted black or white. Find all ways to color the board such that each square of $$2 cm \times 2 cm$$ formed by $$4$$ little squares with a common vertex has $$2$$ black squares and $$2$$ whitesquares.

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