1. Consider the following infinite sequence of boards: Q1 Q2 Q3 Q4 Q5 Q6 So if...

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1. Consider the following infinite sequence of boards: Q1 Q2 Q3 Q4 Q5 Q6 So if n is odd, we obtain Qn+1 by adding one square below the bottom-right of Qn, and if n is even, we obtain Qn+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 R(X) and R2(X). b) Show that Rn(X) = Rn-1(X) + XRn-2(X) for n 3. Using this recursion (or otherwise), give Rn(X) for n = 3, 4, 5, 6, 7. 1. Consider the following infinite sequence of boards: Q1 Q2 Q3 Q4 Q5 Q6 So if n is odd, we obtain Qn+1 by adding one square below the bottom-right of Qn, and if n is even, we obtain Qn+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 R(X) and R2(X). b) Show that Rn(X) = Rn-1(X) + XRn-2(X) for n 3. Using this recursion (or otherwise), give Rn(X) for n = 3, 4, 5, 6, 7.