If you have a line with n segments, how many ways can you color it with the colors Green, Blue and Red, if there are no adjacent blue segments?
My answer is $ 2a_{n-1} + a_{n-2} $
My reasoning:
Possibilities
______________G (n-1)
______________R (n-1)
______________B (n-1-1 = n-2 (Don't count the BB ending)