Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.2

Tiling a (2 × n)-Board with Squares and Dominoes

Matt Katz
Pennsylvania State University
Mathematics Department
109 McAllister Building
University Park, PA 16802

Catherine Stenson
Juniata College
1700 Moore Street
Huntingdon, PA 16652


The Fibonacci numbers and the Pell numbers can be interpreted as the number of tilings of a (1 × n)-board by colored squares and dominoes. We explore the tilings of (2 × n)-boards by colored squares and dominoes. We develop a recurrence relation and prove several combinatorial identities in the style of recent work by Benjamin and Quinn. We also give a bijection between these (2 × n)-tilings and a set of weighted (1 × n)-tilings.

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(Concerned with sequence A000045 A000129 and A030186.)

Received November 20 2008; revised version received January 14 2009. Published in Journal of Integer Sequences, January 16 2009.

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