A343577 Number of generalized polyforms on the truncated square tiling with n cells.

1, 2, 2, 7, 22, 93, 413, 2073, 10741, 57540, 312805, 1722483, 9564565, 53489304, 300840332, 1700347858, 9650975401

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.

a(n) >= A343417(n), the number of (n-k)-polyominoes with k distinguished vertices.

Links

Table of n, a(n) for n=0..16.

Peter Kagey, Haskell program for computing sequence.

Peter Kagey, The a(3) = 7 generalized polyforms on the truncated square tiling with 3 cells.

John Mason, Illustration of equivalence between truncated square polyforms and a mixture of crosses and squares.

Wikipedia, Truncated Square 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).

Sequence in context: A156464 A156520 A307426 * A342644 A069101 A221648

Adjacent sequences: A343574 A343575 A343576 * A343578 A343579 A343580

Keyword

nonn,more

Author

Peter Kagey, Apr 20 2021

Extensions

a(11) from Drake Thomas, May 02 2021

a(12)-a(16) from John Mason, Mar 20 2022

Status

approved