cp's OEIS Frontend

A361288 Number of free polyominoes of size 2n for which there exists at least one closed path that passes through each square exactly once.

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