%I #27 May 01 2021 22:10:05
%S 1,2,2,9,40,218,1377,9285,65039,465888
%N Number of generalized polyforms on the truncated hexagonal tiling with n cells.
%C Equivalently, the number of polyhexes with n-k cells and k distinguished vertices.
%C This sequence counts "free" polyforms where holes are allowed. This means that two polyforms are considered the same if one is a rigid transformation (translation, rotation, reflection or glide reflection) of the other.
%H Peter Kagey, <a href="/A343406/a343406.hs.txt">Haskell program for computing sequence</a>.
%H Peter Kagey, <a href="/A343406/a343406.pdf">The a(3) = 9 generalized polyforms on the truncated hexagonal tiling with 3 cells</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_hexagonal_tiling">Truncated hexagonal tiling</a>
%Y Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343577 (truncated square).
%K nonn,more,hard
%O 0,2
%A _Peter Kagey_, Apr 14 2021