Question

a) Find a recurrence relation for the number of ways to
lay out a walkway with slate tiles if the tiles are red,
green, or gray, so that no two red tiles are adjacent and
tiles of the same color are considered indistinguish-
able.
b) What are the initial conditions for the recurrence re-
lation in part (a)?
c) How many ways are there to lay out a path of seven
tiles as described in part (a)?