[seqfan] Re: L-connected polyominoes

[Tom Duff]

I don’t know what an “L” is in this context. At first I thought it would be
the tromino that isn’t a straight line. But that doesn’t jibe with your
counts. I also can’t figure out from your description what the skew
tetromino is.

On Sun, Jan 22, 2023 at 9:49 PM Allan Wechsler <acwacw at gmail.com> wrote:

> The following seems like as idea that must be in OEIS already, but I have
> been unable to assemble enough data (that I actually believe) to find it.
>
> In some free polyominoes, every pair of cells is part of an "L" that is
> also part of the polyomino. The smallest polyomino that *isn't *connected
> in this way is the skew tetromino, whose end cells cannot be connected by
> an "L".
>
> I am pretty sure that the census of L-connected polyominoes begins: 1
> monomino; 1 domino; 2 trominoes; 4 tetrominoes; and 7 pentominoes (out of
> 12). I am not sure about hexominoes, but my current best guess is 13. OEIS
> reports dozens of matches to this sequence of values.
>
> Do any of the assembled intellects of SeqFan remember running into
> something like this? Or is your searching ability better than mine? (Or can
> you compute the number of hexominoes and heptominoes confidently enough to
> nail it down?)
>
> Thanks in advance!
>
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