Consider a sequence of length n consisting of only three distinct characters: A, B, and C. Let's say a sequence is "beautiful" if it does not contain any consecutive subsequence of "ABC" in it. For example: AAB, BCA, ACB, CCCA are beautiful sequences. AABC, CABC, ABCAA are not beautiful sequences. For a given n, find the number of "beautiful" sequences of length n.

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