A343406 Number of generalized polyforms on the truncated hexagonal tiling with n cells.

1, 2, 2, 9, 40, 218, 1377, 9285, 65039, 465888, 3385778, 24864272, 184115213, 1372589329, 10291503008, 77544953479

Offset: 0

Author

Peter Kagey, Apr 14 2021

Keywords

• nonn
• more
• hard

Comments

Equivalently, the number of polyhexes with n-k cells and k distinguished vertices.

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(3) = 9 generalized polyforms on the truncated hexagonal tiling with 3 cells.
• Wikipedia, Truncated hexagonal 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), A343577 (truncated square).

Extensions

a(10)-a(15) from Bert Dobbelaere, Jun 06 2025