Suppose you have large collections of red 1 * 2 tiles, blue 1 * 2 tiles

and green 1 * 2 tiles. For n >= 0, let tn be the number of ways to use

these to (exactly) cover the squares of a 2 * n checkerboard (i.e., without

overlapping of tiles). Note that tiles can be placed on the board either

vertically or horizontally.

(a) Determine t0, t1, t2 and t3.

(b) Find a recurrence relation and initial conditions for tn.