[seqfan] Re: Maximum-area farm on a square grid

[Allan Wechsler]

I think Franklin has nailed it. This is the correct sequence, with an
indexing change, as noted in the 2015 comment from Juhani Heino. I think I
didn't find it because I neglected to try eliminating leading zeroes.

On Fri, Jun 30, 2023 at 11:24 AM Neil Sloane <njasloane at gmail.com> wrote:

> Franklin, Are you saying that A001971 is the right answer, and Allan W.'s
> A(10)=8 is wrong? If so, could you add a comment to A001971 giving that
> interpretation?
>
> Or maybe you just meant that A001971 deals with a similar problem, but not
> exactly the same problem?
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Fri, Jun 30, 2023 at 1:10 AM Frank Adams-watters via SeqFan <
> seqfan at list.seqfan.eu> wrote:
>
> > A001971
> >
> > Franklin T. Adams-Watters
> >
> >
> >     On Thursday, June 29, 2023 at 11:02:29 PM CDT, Allan Wechsler <
> > acwacw at gmail.com> wrote:
> >
> >  On an infinite chessboard, you are allowed to mark N cells, with the aim
> > of
> > enclosing an area of maximal size. If you are allowed to mark 8 cells,
> for
> > example, then I think the best you can do is to enclose 5 cells.
> >
> > (By "enclose", I mean that you can't escape from an interior cell to the
> > outside world by a path consisting of orthogonal unit moves that never
> > visit a marked cell.)
> >
> > With less than 4 marks, you can't enclose *any* cells, so I think this
> > function has the first few values A(1) = A(2) = A(3) = 0, A(4) = A(5) =
> 1,
> > A(6) = 2, A(7) = 3, A(8) = 5. I am not completely certain, but I *think
> > *A(9)
> > = 6 and A(10) = 8. If these values are correct then I don't think the
> > sequence is in OEIS yet, which surprises me because it seems like an
> > obvious problem.
> >
> > Obviously we expect roughly quadratic growth here. A011864 has the right
> > first few values but if that's the right formula I'll be mighty
> surprised!
> >
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> >
> >
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