1. Consider the following infinite sequence of boards: . . . Q1 Q 2 Q3 Q4 Q5 Q6 So if n is odd, we obtain On+1 by adding one square below the bottom-right of Qn, and if n is even, we obtain On+1 by adding one square to the right of the bottom-right of Qn. Define Rn(X) to be the rook polynomial of Qn. a) Find Ri(X) and R2(X). b) Show that Rn(X) = Rn-1(X) + XRn-2(X) for n 2 3. c) Using this recursion (or otherwise), give Rn(X ) for n = 3, 4, 5, 6, 7