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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, 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
+-+ +-+
| | | |
+ +-+ +-+
| |
+-+-+-+-+
and
+-+-+-+
| |
+ +-+ +-+
| | | |
+-+ +-+-+
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
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