A277565 Number of flattenable free polyominoids.

1, 2, 7, 40, 281, 2538

Offset: 1

Author

John Mason, Oct 20 2016

Keywords

• nonn
• more

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.

Links

• John Mason, Drawings of flattenable and unflattenable polyominoids

Crossrefs

Cf. A075679.