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

Offset

0,2

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

Table of n, a(n) for n=0..15.

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).

Sequence in context: A006445 A174255 A254199 * A097949 A268572 A343909

Adjacent sequences: A343395 A343396 A343397 * A343399 A343400 A343401

Keyword

nonn,more,hard

Author

Peter Kagey, Apr 13 2021

Extensions

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

Status

approved