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Let an be the number of strings of symbols {a,b,c,1,2,3} of length n, such that exactly one of the symbols in a string is a

Let an be the number of strings of symbols {a,b,c,1,2,3} of length n, such that exactly one of the symbols in a string is a digit. Find the generating function of the sequence an. Your answer should be a ratio of two polynomials.

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