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

[Neil Sloane]

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!
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>