Summary: In this paper we give recursive formulas for the number of colorful tilings of small rectangular arrays. We enumerate the tilings of a $2 \times n$ board with painted squares, dominoes, and I-trominoes. We also provide a recursion formula for the number of tilings of a $3 \times n$ board with colorful squares and dominoes. Finally, we describe a general method for calculating the number of colorful tilings of an $m \times n$ board with squares and dominoes.

05B45, 05A15, 52C20

domino, tiling, I-tromino, transfer matrix