A367173 a(n) = the maximum number of distinct tilings of a polyomino of size n using any combination of polyomino tiles of sizes 1 through n.

1, 2, 4, 12, 24, 74, 148, 456, 1434, 2868, 8832, 27780

Offset: 1

Author

John Mason from an idea of Craig Knecht, Nov 07 2023

Keywords

• nonn
• more

Comments

The sequence considers reflections and rotations as distinct tilings.

The polyominoes being tiled and the tiles themselves may be with or without holes.

Examples

			a(3) = 4 because any tromino can be tiled by (1) a tromino, (2) 3 monominoes, and (3) a monomino and a domino in two distinct ways.
		

Crossrefs

Cf. A000105, A367172, A367174.