[seqfan] L-connected polyominoes

[Allan Wechsler]

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!