%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