Let's call a ternary string good provided it never contains a 2 followed immediately by a 0. Let \(G_n\) be the number of good strings of length \(n\text{.}\) For example, \(G_1 = 3\text{,}\) and \(G_2 = 8\) (since of the 9 ternary strings of length 2, only one is not good).
in-context