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

[John Mason]

Allan
Thanks, that's right. I changed my test to:
convex, with 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, and a perimeter that forms a self-avoiding polygon of bracelet
length 8.
Now I get the same figures.

Don. For a(8) I think you're missing

OOOO

OOO_
__O_

On Wed, Feb 1, 2023 at 4:16 PM Allan Wechsler <acwacw at gmail.com> wrote:

> 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/
> >
>
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