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%I #13 Apr 21 2026 09:07:45
%S 1,13,88,1035,11889,148658
%N a(n) is the number of free polydoms of size n.
%C 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.
%C 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.
%H Bernd Karl Rennhak, <a href="http://www.logelium.de/DiDom/DomUndIno_EN.htm">Polydom</a>.
%H George Sicherman, <a href="https://sicherman.net/kites-bricks/index.html">Didom Kites and Bricks</a>.
%Y Cf. A006074.
%K nonn,more,hard
%O 1,2
%A _John Mason_, Apr 19 2026