Geodesic
Tiling a ($2 \times n$)-board with squares and dominoes
Journal of integer sequences, Tome 12 (2009) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The Fibonacci numbers and the Pell numbers can be interpreted as the number of tilings of a ($1 \times n$)-board by colored squares and dominoes. We explore the tilings of ($2 \times n$)-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 ($2 \times n$)-tilings and a set of weighted ($1 \times n$)-tilings.
Classification : 05A19, 05A15, 05B45
Keywords: dominoes, tiling, Fibonacci numbers, pell numbers 
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     title = {Tiling a ($2 \times n$)-board with squares and dominoes},
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Katz, Matt; Stenson, Catherine. Tiling a ($2 \times n$)-board with squares and dominoes. Journal of integer sequences, Tome 12 (2009) no. 2. http://geodesic.mathdoc.fr/item/JIS_2009__12_2_a7/