cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A277565 Number of flattenable free polyominoids.

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%I A277565 #13 Oct 20 2016 12:37:27
%S A277565 1,2,7,40,281,2538
%N A277565 Number of flattenable free polyominoids.
%C A277565 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".
%C A277565 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.
%C A277565 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.
%C A277565 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.
%H A277565 John Mason, <a href="/A277565/a277565.pdf">Drawings of flattenable and unflattenable polyominoids</a>
%Y A277565 Cf. A075679.
%K A277565 nonn,more
%O A277565 1,2
%A A277565 _John Mason_, Oct 20 2016