A344213 Number of generalized polyforms on the truncated trihexagonal tiling with n cells.

1, 3, 3, 14, 50, 261, 1397, 8364, 50643, 315512, 1984853, 12619579, 80802300, 520724842, 3373646060, 21959949924, 143527242317

Offset: 0

Author

Peter Kagey, May 11 2021

Keywords

• nonn
• hard
• 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.

Links

• Peter Kagey, Illustration of a(3) = 14.
• Wikipedia, Truncated trihexagonal 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), A344211 (rhombitrihexagonal).

Extensions

a(10)-a(16) from Bert Dobbelaere, Jun 07 2025