Let h_n denote the number of ways to color the squares of a 1-by-n board with the colors red, white, blue, and green in such a way that the number of squares colored red is even and the number of squares colored white is odd. Determine the exponential generating function for the sequence h_0, h_1, h_2, ..., h_n, ..., and then find a simple formula for h_n.
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