Geodesic
Tiling with L's and squares
Journal of integer sequences, Tome 10 (2007) no. 2.

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

Summary: We consider tilings of $2 \times n, 3 \times n$, and $4 \times n$ boards with $1 \times 1$ squares and L-shaped tiles covering an area of three square units, which can be used in four different orientations. For the $2 \times n$ board, the recurrence relation for the number of tilings is of order three and, unlike most third order recurrence relations, can be solved exactly. For the $3 \times n$ and $4 \times n$ board, we develop an algorithm that recursively creates the basic blocks (tilings that cannot be split vertically into smaller rectangular tilings) of size $3 \times k$ and $4 \times k$ from which we obtain the generating function for the total number of tilings. We also count the number of L-shaped tiles and $1 \times 1$ squares in all the tilings of the $2 \times n$ and $3 \times n$ boards and determine which type of tile is dominant in the long run.
Keywords: tilings, trominoes, recurrence relations, generating functions 
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     title = {Tiling with {L's} and squares},
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     number = {2},
     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a6/}
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Chinn, Phyllism; Grimaldi, Ralph; Heubach, Silvia. Tiling with L's and squares. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a6/