Geodesic
Counting colorful tilings of rectangular arrays
Journal of integer sequences, Tome 20 (2017) no. 5
In this paper we give recursive formulas for the number of colorful tilings of small rectangular arrays. We enumerate the tilings of a $2 \times n$ board with painted squares, dominoes, and I-trominoes. We also provide a recursion formula for the number of tilings of a $3 \times n$ board with colorful squares and dominoes. Finally, we describe a general method for calculating the number of colorful tilings of an $m \times n$ board with squares and dominoes.
Classification : 05B45, 05A15, 52C20
Keywords: domino, tiling, I-tromino, transfer matrix 
@article{JIS_2017__20_5_a4,
     author = {Haymaker,  Kathryn and Robertson,  Sara},
     title = {Counting colorful tilings of rectangular arrays},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {5},
     zbl = {1365.05042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a4/}
}
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AU  - Robertson,  Sara
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%A Robertson,  Sara
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%J Journal of integer sequences
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Haymaker,  Kathryn; Robertson,  Sara. Counting colorful tilings of rectangular arrays. Journal of integer sequences, Tome 20 (2017) no. 5. http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a4/