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
USA
Abstract:
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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