How would I find the characteristic equation of this Recurrence Relation? Find and solve a recurrence relation for the number of $n$-digit ternary sequences with no consecutive digits being equal.
Since for ternary, meaning only $3$ possible entries for each space, e.g. $0$, $1$, $2$, the first slot $n$ has $3$ possible choices and then each position before ($n-1$, $n-2$, $\ldots$ , $2$, $1$) have $2$ choices each, I got the following recurrence relation:$$a_n=2\cdot a_{n-1}$$
Now I am trying to solve the homogeneous linear recurrence model, but I am stuck in finding a characteristic equation. How would I do this?

Doubling every time should not require a characteristic equation! However, it is $x-2=0$.
