cp's OEIS Frontend

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.

The coordination sequence for polyominoid cells (row 18 of A366768) is A005914, except that the term for distance 1 should be 12.

If d > n+1, there are T(n,n+1) such polyominoids. The triangle only includes the values for d <= n+1.