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

0,2

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..16.

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).

Sequence in context: A367672 A298960 A356117 * A243545 A387248 A094152

Adjacent sequences: A344210 A344211 A344212 * A344214 A344215 A344216

Keyword

nonn,hard,more

Author

Peter Kagey, May 11 2021

Extensions

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

Status

approved