A366335 Number of fixed (4,2)-polyominoids with n cells.

6, 60, 916, 16698, 336210, 7218768, 162185112, 3769221330, 89924613880

Offset: 1

Author

Pontus von Brömssen, Oct 07 2023

Keywords

• nonn
• hard
• more

Comments

A (D,d)-polyominoid is a connected set of d-dimensional unit cubes with integer coordinates in D-dimensional space, where two cubes are connected if they share a (d-1)-dimensional facet. For example, (3,2)-polyominoids are normal polyominoids (A075678), (D,D)-polyominoids are D-dimensional polyominoes (A001168, A001931, A151830, ...), and (D,1)-polyominoids are polysticks in D dimensions (A096267, A365560, A365562, ...).

Links

• Wikipedia, Polyominoid.
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A366334 (free).

46th row of A366767.

Fixed (D,d)-polyominoids:

D\d| 1 2 3 4

---+--------------------------------

1 | A000012

2 | A096267 A001168

3 | A365560 A075678 A001931

4 | A365562 A366335 A366337 A151830

Extensions

a(7)-a(9) from John Mason, Jul 05 2025