Tiling a (2 × n)-Board with Squares and Dominoes
Matt Katz
Pennsylvania State University
Mathematics Department
109 McAllister Building
University Park, PA 16802
USA
Catherine Stenson
Juniata College
1700 Moore Street
Huntingdon, PA 16652
USA
Abstract:
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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