A270061 Number A(n,k) of tilings of a k X n rectangle using monominoes and trominoes of any shape; square array A(n,k), n>=0, k>=0, read by antidiagonals.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 3, 14, 14, 3, 1, 1, 4, 45, 93, 45, 4, 1, 1, 6, 140, 590, 590, 140, 6, 1, 1, 9, 438, 3710, 7517, 3710, 438, 9, 1, 1, 13, 1371, 23509, 96176, 96176, 23509, 1371, 13, 1, 1, 19, 4287, 148796, 1238818, 2501946, 1238818, 148796, 4287, 19, 1
Offset: 0
Examples
A(2,3) = A(3,2) = 14: ._____. ._____. ._____. ._____. ._____. ._____. ._____. |_____| |_|_|_| |_____| |_| |_| | |_|_| | ._|_| |_. |_| |_____| |_____| |_|_|_| |___|_| |___|_| |_|_|_| |_|_|_| . ._____. ._____. ._____. ._____. ._____. ._____. ._____. |_|_|_| | ._| | | |_. | |_|_| | |_| |_| |_| ._| |_|_. | |_|_|_| |_|___| |___|_| |_|___| |_|___| |_|_|_| |_|_|_| . . Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 2, 3, 4, 6, ... 1, 1, 5, 14, 45, 140, 438, ... 1, 2, 14, 93, 590, 3710, 23509, ... 1, 3, 45, 590, 7517, 96176, 1238818, ... 1, 4, 140, 3710, 96176, 2501946, 65410388, ... 1, 6, 438, 23509, 1238818, 65410388, 3473827027, ...
Links
- Liang Kai, Antidiagonals n = 0..35, flattened (antidiagonals n = 0..25 from Alois P. Heinz)
- Wikipedia, Tromino