A344211 Number of generalized polyforms on the rhombitrihexagonal tiling with n cells.

1, 3, 2, 7, 16, 60, 201, 838, 3407, 14767, 64200, 284676, 1269981, 5715325, 25854146, 117576949, 536918541, 2461230475, 11319321354, 52212782646

Offset: 0

Author

Peter Kagey, May 11 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

• Kadon Enterprises, Birds and Bees.
• Peter Kagey, Illustration of a(3) = 7.
• George Sicherman, Catalogue of Polybirds.
• Wikipedia, Rhombitrihexagonal tiling
• Livio Zucca, PolyTriForms.

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(11)-a(19) from Bert Dobbelaere, Jun 05 2025