A344211 Number of generalized polyforms on the rhombitrihexagonal tiling with n cells.

1, 3, 2, 7, 16, 60, 201, 838, 3407, 14767, 64200, 284676, 1269981, 5715325, 25854146, 117576949, 536918541, 2461230475, 11319321354, 52212782646

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..19.

Kadon Enterprises, Birds and Bees.

Peter Kagey, Illustration of a(3) = 7.

George Sicherman, Catalogue of Polybirds.

Wikipedia, Rhombitrihexagonal tiling

Livio Zucca, PolyTriForms.

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).

Sequence in context: A049968 A363399 A049970 * A104528 A177115 A316087

Adjacent sequences: A344208 A344209 A344210 * A344212 A344213 A344214

Keyword

nonn,more,hard

Author

Peter Kagey, May 11 2021

Extensions

a(11)-a(19) from Bert Dobbelaere, Jun 05 2025

Status

approved