%I #23 May 01 2024 11:28:42

%S 1,2,4,8,16,58,116,232,464,1690,3380,6760,24712,49424,98848,361258,

%T 722516,1445032,5280576,10561152,21122304,77188216

%N 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.

%C The sequence considers reflections and rotations as distinct tilings.

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

%H Craig Knecht, John Mason and Walter Trump, <a href="/A367172/a367172_1.pdf">Polyiamond tiling V2</a>

%e 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.

%Y Cf. A000577, A367173, A367174.

%K nonn,more

%O 1,2

%A _Craig Knecht_ and _John Mason_, Nov 07 2023

%E More terms from _Walter Trump_, May 01 2024