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
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.
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).
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
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
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).
A345076
Number of generalized polyforms on the elongated triangular tiling with n cells.
Original entry on oeis.org
1, 2, 3, 5, 13, 32, 96, 283, 907, 2929, 9787, 32939, 112476, 386230, 1336150, 4642930, 16208851, 56786242, 199614651, 703678568, 2487109359, 8811020024, 31281360326, 111272475650
Offset: 0
See the PDF in the links section.
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).
A350739
Number of polykagomes with n cells, distinguishing mirror images.
Original entry on oeis.org
2, 1, 4, 14, 47, 178, 697, 2746, 11071, 45093, 185341, 767786, 3201291, 13420045, 56524684
Offset: 1
On the trihexagonal grid, a triangle can be adjacent only to a hexagon and vice versa. The only shape with 2 cells is a triangle joined to a hexagon, so a(2) = 1.
Cf.
A343398, which identifies mirror images.
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