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A277565
Number of flattenable free polyominoids.
2
1, 2, 7, 40, 281, 2538
OFFSET
1,2
COMMENTS
A polyominoid is flattenable if, by a process of unfolding, it may be transformed into a polyomino with the same number of squares. Tearing is not allowed - if two squares are adjacent in the polyominoid, they must be adjacent in the polyomino. Overlapping squares are not allowed - the polyomino must be exactly "one square thick".
To avoid ambiguity, the squares are infinitely flexible during the unfolding process; this is important for large polyominoids that thread through themselves. On the other hand, a polyominoid containing two intersecting rings is obviously not flattenable.
It is interesting that flattening is not a reversible process. In many cases, the resulting polyomino may not be folded to produce the original polyominoid without tearing.
See the link for drawings of the polyominoes of sizes 1 through 5, and all polyominoids that will flatten to those shapes. At the end of the file are all polyominoids of sizes 1 through 5 that are not flattenable.
CROSSREFS
Cf. A075679.
Sequence in context: A189826 A069732 A346964 * A157504 A093985 A308876
KEYWORD
nonn,more
AUTHOR
John Mason, Oct 20 2016
STATUS
approved