Geodesic
The tilings of a (\(2 \times \) n)-board and some new combinatorial identities
Journal of integer sequences, Tome 20 (2017) no. 5
We know that the Fibonacci numbers count the tilings of a ($1 \times n$)-board by squares and dominoes, or equivalently, the number of tilings of a ($2 \times n$)-board by dominoes. We use the tilings of a ($2 \times n$)-board by colored unit squares and dominoes to obtain some new combinatorial identities. They are generalization of some known combinatorial identities and in the special case give us the Fibonacci identities.
Classification : 05A19, 05A15, 05B45, 11B39
Keywords: domino, tiling, Fibonacci number, combinatorial identity 
@article{JIS_2017__20_5_a7,
     author = {Kahkeshani,  Reza},
     title = {The tilings of a (\(2 \times \) n)-board and some new combinatorial identities},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {5},
     zbl = {1361.05016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a7/}
}
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Kahkeshani,  Reza. The tilings of a (\(2 \times \) n)-board and some new combinatorial identities. Journal of integer sequences, Tome 20 (2017) no. 5. http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a7/