Geodesic
Tiling a \((2 \times n)\)-board with squares and dominoes
Journal of integer sequences, Tome 12 (2009) no. 2
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 
@article{JIS_2009__12_2_a7,
     author = {Katz,  Matt and Stenson,  Catherine},
     title = {Tiling a \((2 \times n)\)-board with squares and dominoes},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {2},
     zbl = {1228.05062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_2_a7/}
}
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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/