How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same?
Not sure if I understood the question correctly. It's asking for possible 10 digit number with $0, 1, 2$ and no consecutive digits.
My thoughts are if there are 10 spaces then the first space will be $3\choose 1$, second one cannot be the same with the first one so it will have to be $2\choose 1$.
So it will come down to $3\times 2^9$. Can someone correct if I'm wrong ?