finding a recurrence relation for tile covering problem

Question

for $n \ge 1$ let $t_n$ be the number of ways to.cover the squares of a 2xn xheckerboard using 1x2 tiles which can be rotated (ie 2x1 tile) and 2x2 tiles. 1x2 tile comes in 5 different colors and 2x2 tile in 4 different colors. find and solve a recurrence relation for $t_n$