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%I #21 Mar 09 2023 02:15:26
%S 1,1,3,6,25,84,397,1855,9708,51684,286011,1609097,9222409,53543338,
%T 314612803
%N Number of free polyominoes of size 2n for which there exists at least one closed path that passes through each square exactly once.
%C A polyomino for which more than one closed path exists counts as 1. On the other hand, in A266549, distinct closed paths count separately. For example for n=7, this latter sequence distinguishes between
%C +-+ +-+
%C | | | |
%C + +-+ +-+
%C | |
%C +-+-+-+-+
%C and
%C +-+-+-+
%C | |
%C + +-+ +-+
%C | | | |
%C +-+ +-+-+
%H John Mason, <a href="/A361288/a361288.pdf">Examples</a>
%e For n = 4 the a(4) = 3 solutions are:
%e XXX XX XXXX
%e X X XXX XXXX
%e XXX XXX
%Y Cf. A266549 (where distinct closed paths count separately).
%K nonn,more,hard
%O 2,3
%A _John Mason_ and _Tanya Khovanova_, Mar 07 2023
%E a(13) - a(16) from _Bert Dobbelaere_, Mar 09 2023
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