(a) For n ∈ Z+, determine the number of ways one can tile a 1 × n chessboard using 1 × 1 white (square) tiles and 1×2 blue (rectangular) tiles.
(b) How many of the tilings in part (a) use (i) no blue tiles; (ii) exactly one blue tile; (iii) exactly two blue tile&? (iv) exactly three blue tiles; and (v) exactly k blue tiles, where 0 ≤ k ≤ [n/2]?
(c) How are the results in parts (a) and (b) related?