cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A344213 Number of generalized polyforms on the truncated trihexagonal tiling with n cells.

Original entry on oeis.org

1, 3, 3, 14, 50, 261, 1397, 8364, 50643, 315512, 1984853, 12619579, 80802300, 520724842, 3373646060, 21959949924, 143527242317
Offset: 0

Views

Author

Peter Kagey, May 11 2021

Keywords

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.

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).

Extensions

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

A383908 Number of generalized polyforms with n cells on the snub trihexagonal tiling.

Original entry on oeis.org

1, 3, 3, 7, 23, 69, 228, 766, 2642, 9309, 33382, 120629, 439752, 1613135, 5953061, 22075011, 82204128, 307213215, 1151820825, 4330858682, 16326297768, 61690058385
Offset: 0

Views

Author

Peter Kagey, May 14 2025

Keywords

Comments

A generalized polyform on the snub trihexagonal tiling with n-cells is a collection of n faces connected edgewise. Two polyforms are considered the same they are related by an isometry (translation and/or rotation) of the snub trihexagonal tiling.

Examples

			For n=1, the a(1) = 3 generalized polyforms are the three types of faces: hexagons, hexagon-adjacent triangles, and hexagon-nonadjacent triangles.
For n=2, the a(2) = 3 generalized polyforms are
(1) a hexagon with a hexagon-adjacent triangle,
(2) a hexagon-adjacent triangle with a hexagon-nonadjacent triangle, and
(3) two hexagon-adjacent triangles.
		

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), A344213 (truncated trihexagonal).

Extensions

a(12)-a(21) from Bert Dobbelaere, Jun 05 2025

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

Original entry on oeis.org

1, 2, 4, 13, 53, 209, 904, 3963, 17900, 81745, 378554, 1768236, 8327789, 39471091, 188145066, 901117082, 4334151970, 20923370406, 101341800704, 492289834345
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

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.

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).

A385266 Number of edge-connected components of polygonal cells in the basketweave tiling up to rotation and reflection of the tiling.

Original entry on oeis.org

1, 2, 2, 10, 34, 166, 777, 4053, 21225, 114594, 624242, 3442399, 19121661, 106964679, 601639326, 3400619170, 19301719485, 109962791254
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

Each square cell in the basketweave tiling is edge-connected to four rectangular 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), A385265 (pinwheel).
Showing 1-4 of 4 results.