11. You have access to 1 × 1 tiles which come in 2 different colors and 1 × 2 tiles which come in 3 different colors. We want to figure out how many different 1 x n path designs we can make out of these tiles. (a) Find a recursive definition for the number of paths of length n. (b) Solve the recurrence relation using the Characteristic Root tech- nique.

Fig: 1