A345076 - OEIS

%I #13 Jun 13 2021 15:29:45

%S 1,2,3,5,13,32,96,283,907,2929,9787,32939,112476,386230,1336150

%N Number of generalized polyforms on the elongated triangular tiling with n cells.

%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="/A345076/a345076.pdf">The a(3) = 5 generalized polyforms on the elongated triangular tiling with 3 cells</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_triangular_tiling">Elongated Triangular Tiling</a>

%e See the PDF in the links section.

%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), A343406 (truncated hexagonal), A343577 (truncated square).

%K nonn,more

%O 0,2

%A _Drake Thomas_, Jun 07 2021