A345076 Number of generalized polyforms on the elongated triangular tiling with n cells.

1, 2, 3, 5, 13, 32, 96, 283, 907, 2929, 9787, 32939, 112476, 386230, 1336150, 4642930, 16208851, 56786242, 199614651, 703678568, 2487109359, 8811020024, 31281360326, 111272475650

Offset: 0

Author

Drake Thomas, Jun 07 2021

Keywords

• nonn
• more

Comments

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.

Examples

			See the PDF in the links section.
		

Links

• Peter Kagey, The a(3) = 5 generalized polyforms on the elongated triangular tiling with 3 cells.
• Wikipedia, Elongated Triangular Tiling

Crossrefs

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).

Extensions

a(15)-a(23) from Bert Dobbelaere, Jun 05 2025