A385265 Number of edge-connected components of polygonal cells in the pinwheel tiling up to rotation of the tiling.

1, 2, 4, 13, 53, 209, 904, 3963, 17900, 81745, 378554, 1768236, 8327789, 39471091, 188145066, 901117082, 4334151970, 20923370406, 101341800704, 492289834345

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

• nonn
• more
• hard

Comments

These are "one-sided" polyforms because there are no reflectional symmetries of the pinwheel tiling.

Here the "pinwheel tiling" is a tiling consisting of rectangular and square cells, and does not refer to non-periodic triangular tilings.

Links

• Peter Kagey, Illustration of the pinwheel tiling.
• Peter Kagey, Illustration of the a(4)=53 polyforms with 4 cells.

Crossrefs

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), A344213 (truncated trihexagonal), A383908 (snub trihexagonal), A385266 (basketweave).