Geodesic
On counting the number of tilings of a rectangle with squares of size 1 and 2
Journal of integer sequences, Tome 20 (2017) no. 2
We consider tilings of a rectangle of size $n \times k$ with square tiles of size $1 \times 1$ and $2 \times 2$. We present a method to calculate the number of such tilings via matrix multiplication, where we optimize the number of multiplications needed and reduce the space required for the matrix multiplication by dynamically generating the matrices involved.
Classification : 68R05, 68Q25
Keywords: tiling, analysis of algorithms, combinatorics 
@article{JIS_2017__20_2_a1,
     author = {Nilsson,  Johan},
     title = {On counting the number of tilings of a rectangle with squares of size 1 and 2},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1402.05033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a1/}
}
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Nilsson,  Johan. On counting the number of tilings of a rectangle with squares of size 1 and 2. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a1/