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

1, 1, 3, 6, 25, 84, 397, 1855, 9708, 51684, 286011, 1609097, 9222409, 53543338, 314612803

Offset: 2

Author

John Mason and Tanya Khovanova, Mar 07 2023

Keywords

• nonn
• more
• hard

Comments

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

+-+ +-+

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+ +-+ +-+

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+-+-+-+-+

and

+-+-+-+

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+ +-+ +-+

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+-+ +-+-+

Examples

			For n = 4 the a(4) = 3 solutions are:
  XXX    XX   XXXX
  X X   XXX   XXXX
  XXX   XXX
		

Links

• John Mason, Examples

Crossrefs

Cf. A266549 (where distinct closed paths count separately).

Extensions

a(13) - a(16) from Bert Dobbelaere, Mar 09 2023