Journal of Integer Sequences, Vol. 24 (2021), Article 21.1.2

Fault-Free Tilings of the 3 × n Rectangle With Squares and Dominos

Oluwatobi Jemima Alabi
Government Science Secondary School
Pyakasa, Abuja

Greg Dresden
Washington & Lee University
Lexington, VA 24450


A (completely) fault-free tiling of a board is a tiling with no vertical or horizontal faults. We find a fourth-order recurrence relation for the number of ways to tile such a board using squares and dominos, and we do the same for a vertical-fault-free board (which could have horizontal faults).

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(Concerned with sequences A030186 A033506 A112577 A124997 A334396 A335747.)

Received July 9 2020; revised versions received October 20 2020; December 22 2020. Published in Journal of Integer Sequences, December 28 2020.

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