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

2,3

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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+-+ +-+-+

Links

Table of n, a(n) for n=2..16.

John Mason, Examples

Example

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

Crossrefs

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

Sequence in context: A148661 A148662 A148663 * A266549 A057730 A350752

Adjacent sequences: A361285 A361286 A361287 * A361289 A361290 A361291

Keyword

nonn,more,hard

Author

John Mason and Tanya Khovanova, Mar 07 2023

Extensions

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

Status

approved