A224850 Number T(n,k) of tilings of an n X k rectangle using integer-sided square tiles reduced for symmetry, where the orbits under the symmetry group of the rectangle, D2, have 1 element; triangle T(n,k), k >= 1, 0 <= n < k, read by columns.
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 5, 2, 12, 6, 1, 1, 3, 3, 5, 7, 17, 1, 1, 8, 3, 25, 11, 106, 44
Offset: 1
Examples
The triangle is: n\k 1 2 3 4 5 6 7 8 ... . 0 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 ... 2 1 3 2 5 3 8 ... 3 1 2 2 3 3 ... 4 3 12 5 25 ... 5 6 7 11 ... 6 17 106 ... 7 44 ... ... T(3,5) = 2 because there are 2 different tilings of the 3 X 5 rectangle by integer-sided squares, where any sequence of group D2 operations will only transform each tiling into itself. Group D2 operations are: . the identity operation . rotation by 180 degrees . reflection about a horizontal axis through the center . reflection about a vertical axis through the center The tilings are: ._________. ._________. |_|_|_|_|_| |_| |_| |_|_|_|_|_| |_| |_| |_|_|_|_|_| |_|_____|_|
Links
- Christopher Hunt Gribble, C++ program
Comments