Let fn be the number of strings of length n using the letters A, B, C, D, such that there are an even number of As; 1, 2, 3 or 4 Bs; either 2 or 5 C's; and at least 1 D. So fo = f1 = f2 = f3 = 0, while f4 = 12 and f5 = 60. Find a generating function for fn, and explain how you got it.

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