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Counting Colorful Tilings of Rectangular Arrays

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