Question 100
For $n \ge 2$, consider $n$ boxes aligned from left to right. In each box, one puts a ball that can be red, blue or white such that the following condition is fulfilled: Each box is neighboring at least one box containing a ball of the same color. We denote by $I_n$ the number of such configurations.
a) Determine $I_{11}$. Justify your answer.
b) Find, with proof, the general formula for $I_n$.
a) Determine $I_{11}$. Justify your answer.
b) Find, with proof, the general formula for $I_n$.