A395315 a(n) is the number of free polydoms of size n.

1, 13, 88, 1035, 11889, 148658

Offset

1,2

Comments

A polydom is made of a set of non-overlapping connected doms, where a dom is obtained by cutting a domino (a 2-by-1 rectangle) along its diagonal. The reflection of a dom is also a dom. Two doms are considered as connected if they share an edge or part of an edge as in the following cases: (i) 2 edges of the same length coincide, or (ii) one of the 2 halves of a length 2 edge coincides with a length 1 edge, or with one of the 2 halves of a length 2 edge. See Rennhak link for examples.

Free polydoms are counted according to their footprint. A single polydom may have more than one possible internal construction (like a polytan). Polydoms obtained by rotations, translations and reflections are counted only once.

Links

Table of n, a(n) for n=1..6.

Bernd Karl Rennhak, Polydom.

George Sicherman, Didom Kites and Bricks.

Crossrefs

Cf. A006074.

Sequence in context: A000836 A157771 A289137 * A228481 A277512 A141878

Adjacent sequences: A395312 A395313 A395314 * A395316 A395317 A395318

Keyword

nonn,more,hard

Author

John Mason, Apr 19 2026

Status

approved