Question 7: Let n1 be an integer and consider a 1n board Bn consisting of n cells, each one having side length one. The top part of the figure below shows B9. We have an unlimited supply of bricks which are of the following types (see the bottom part of the figure above): - There are red (R) bricks which are 11 cells. - There are white (W) and blue (B) bricks which are 12 cells. A tiling of a board Bn is a placement of bricks on the board such that: - the bricks exactly cover Bn and - no two bricks overlap. In a tiling and colour can be used more than once and some colours might not be used at all. The figure below shows one possible tiling of B9. Let Tn be the number of different tilings of the board Bn. (a) Determine T1 and T2. (b) Express Tn recursively for n3. (c) Prove that for any integer n1, Tn=31[2n+1+(1)n]