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Number of fixed (4,2)-polyominoids with n cells.
5

%I #9 Dec 04 2023 01:35:19

%S 6,60,916,16698,336210,7218768

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

%C 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, ...).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyominoid">Polyominoid</a>.

%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

%Y Cf. A366334 (free).

%Y 46th row of A366767.

%Y Fixed (D,d)-polyominoids:

%Y D\d| 1 2 3 4

%Y ---+--------------------------------

%Y 1 | A000012

%Y 2 | A096267 A001168

%Y 3 | A365560 A075678 A001931

%Y 4 | A365562 A366335 A366337 A151830

%K nonn,hard,more

%O 1,1

%A _Pontus von Brömssen_, Oct 07 2023