Journal of Integer Sequences, Vol. 20 (2017), Article 17.5.8

Counting Colorful Tilings of Rectangular Arrays

Kathryn Haymaker and Sara Robertson
Villanova University
Department of Mathematics and Statistics
St. Augustine Center 305
800 E. Lancaster Avenue
Villanova, PA 19085


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.

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(Concerned with sequences A030186 A033506 A278815.)

Received December 6 2016; revised version received April 11 2017. Published in Journal of Integer Sequences, June 24 2017.

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