The sequence considers reflections and rotations as distinct tilings.
The polyominoes being tiled and the tiles themselves may be with or without holes.
The number of tilings of a 2-by-n rectangle is 2*
A005668(n). Along with the fact that a(n+1) >= 2*a(n), because any added cell can either remain a monomino, or be joined to a neighboring polyomino, this yields a(1) through a(8). Other shapes take over beginning at a(9). -
Charlie Neder, Sep 10 2025
