Tiling a (2 × n)-Board with Squares and Dominoes
Pennsylvania State University
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University Park, PA 16802
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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.
Full version: pdf,
(Concerned with sequence
Received November 20 2008;
revised version received January 14 2009.
Published in Journal of Integer Sequences, January 16 2009.
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