No ABs in this string

Discrete Mathematics Level 3

A string of \(n\) characters is made from the characters \(\text{A}\), \(\text{B}\), and \(\text{C}\).

Let \(G_n\) be the number of such strings of \(n\) characters which contain no instance of \(\text{AB}\) (in that order).

Write a recurrence relation for \(G_n\).

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