A343398 Number of generalized polyforms on the trihexagonal tiling with n cells.

1, 2, 1, 4, 9, 30, 97, 373, 1405, 5630, 22672, 93045, 384403, 1602156, 6712128, 28268504, 119537113, 507375130, 2160476897, 9226446455, 39504435891

Offset: 0

Author

Peter Kagey, Apr 13 2021

Keywords

• nonn
• more
• hard

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, Haskell program for computing sequence.
• Peter Kagey, The a(4) = 9 generalized polyforms on the trihexagonal tiling with 4 cells.
• Wikipedia, Trihexagonal tiling

Crossrefs

Same but distinguishing mirror images: A350739.

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

Extensions

a(12)-a(15) from John Mason, Mar 04 2022

a(16)-a(20) from Bert Dobbelaere, Jun 06 2025