A367172 a(n) = the maximum number of distinct tilings of a polyiamond of size n using any combination of polyiamond tiles of sizes 1 through n.

1, 2, 4, 8, 16, 58, 116, 232, 464, 1690, 3380, 6760, 24712, 49424, 98848, 361258, 722516, 1445032, 5280576, 10561152, 21122304, 77188216

Offset: 1

Author

Craig Knecht and John Mason, Nov 07 2023

Keywords

• nonn
• more

Comments

The sequence considers reflections and rotations as distinct tilings.

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

Examples

			a(3) = 4 because the triamond can be tiled by (1) a triamond, (2) 3 moniamonds, and (3) a moniamond and a diamond in two distinct ways.
		

Links

• Craig Knecht, John Mason and Walter Trump, Polyiamond tiling V2

Crossrefs

Cf. A000577, A367173, A367174.

Extensions

More terms from Walter Trump, May 01 2024