[seqfan] Re: Help with A028247 Number of T-frame polyominoes with n cells

[Allan Wechsler]

John Mason, your #4 doesn't satisfy what I infer to be Anne Fontaine's
intended constraints.

One way to say it is that the perimeter must be a right angled octagon, and
as you traverse it counterclockwise you encounter turns in the order
LLLLRLLR.

Fontaine is a combinatorial tiling specialist, and has written about
"U-frame" (LLLLLLRR) and "Z-frame" (LLLRLLLR) polyominoes as well.

On Wed, Feb 1, 2023, 4:45 AM John Mason <masonmilan33 at gmail.com> wrote:

> Thanks for everyone's help. That got me through to a(6).
> But now, instead of a(7)=10, I'm getting 11. Which of these is wrong?
> (I am using the following condition: the polyomino must be board-pile,
> convex, have a complete top row (extends over the entire width), and a
> bottom row that starts a bit to the right of the top row and finishes a bit
> to the left)
>
> 1.
> OOO
> OOO
> _O_
>
> 2.
> OOOOO
> _OO__
>
> 3.
> OOOO
> OO__
> _O__
>
> 4.
> OOOO
> _OO_
> _O__
>
> 5.
> OOO
> OO_
> _O_
> _O_
>
> 6.
> OOOOOO
> _O____
>
> 7.
> OOOOOO
> __O___
>
> 8.
> OOOOO
> _O___
> _O___
>
> 9.
> OOOOO
> __O__
> __O__
>
> 10.
> OOOO
> _O__
> _O__
> _O__
>
> 11.
> OOO
> _O_
> _O_
> _O_
> _O_
>
> On Wed, Feb 1, 2023 at 5:38 AM Don Reble via SeqFan <seqfan at list.seqfan.eu
> >
> wrote:
>
> > > XXX
> > > XX.
> > > .X.
> >
> > > ...polyominoes which are integral rectangles with integral notches cut
> > > from two adjacent corners.
> >
> >     I like that take, yielding sequence
> >         0,0,0,1,2,6,10,18,27,42,55,80,101,133,163,211,246,308,353,432,...
> >     but I get a(8)=18 instead of 19, etc. Did I miss one?
> >
> > .XXX. .XX... ..XX.. .X..... ..X.... ...X...
> > XXXXX XXXXXX XXXXXX XXXXXXX XXXXXXX XXXXXXX
> >
> > .XX. .X... .X.... ..X...
> > .XX. XX... .X.... ..X...
> > XXXX XXXXX XXXXXX XXXXXX
> >
> > .X. .X. .X.. .X... ..X..
> > XX. .X. .X.. .X... ..X..
> > XX. XXX XX.. .X... ..X..
> > XXX XXX XXXX XXXXX XXXXX
> >
> > .X. .X..
> > .X. .X..
> > .X. .X..
> > XX. .X..
> > XXX XXXX
> >
> > .X.
> > .X.
> > .X.
> > .X.
> > .X.
> > XXX
> >
> > --
> > Don Reble  djr at nk.ca
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>