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A277565 Number of flattenable free polyominoids. 1
1, 2, 7, 40, 281, 2538 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..6.

John Mason, Drawings of flattenable and unflattenable polyominoids

CROSSREFS

Cf. A075679.

Sequence in context: A189826 A069732 A346964 * A157504 A093985 A308876

Adjacent sequences:  A277562 A277563 A277564 * A277566 A277567 A277568

KEYWORD

nonn,more

AUTHOR

John Mason, Oct 20 2016

STATUS

approved

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Last modified May 28 17:57 EDT 2022. Contains 354120 sequences. (Running on oeis4.)