[seqfan] Re: [Seqfan] A sequence related to Go

Yifan Xie xieyifan4013 at 163.com
Thu Jun 16 03:55:59 CEST 2022

```No, it isn't already in OEIS.
The sequence begins with 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 8, 10, 13, 15, 18.

---- Replied Message ----
| From | Allan Wechsler<acwacw at gmail.com> |
| Date | 06/15/2022 22:34 |
| To | Sequence Fanatics Discussion list<seqfan at list.seqfan.eu> |
| Subject | [seqfan] Re: [Seqfan] A sequence related to Go |
Just substituting small numbers into Yifan Xie's formula suggests that a
board with no corners or edges is being contemplated. On a board with a
corner, two stones can surround one, while the formula gives 0. On a board
with an edge, three stones can surround one, while the formula still gives
0.

On a 19x19 board, one stone can capture 360! So we are definitely talking
about a board that is infinite in all directions.

For those unfamiliar with the rules of Go, the question is, what is the
maximum size of a polyomino with first surround n?

Anyway, the sequence is apparently already in OEIS, at
https://oeis.org/A001971. The comment from Juhani Heino gives the Go
property.

On Wed, Jun 15, 2022 at 5:49 AM Fred Lunnon <fred.lunnon at gmail.com> wrote:

>   Is the board size  19x19  cells?  Or is it infinite?     WFL
>
>
>
> On Wed, Jun 15, 2022 at 9:04 AM Yifan Xie <xieyifan4013 at 163.com> wrote:
>
> > Hi everyone,
> >
> >
> > Is this sequence suitable for OEIS?
> >
> >
> > a(n) is the maximum size of white pieces which can be taken from the
> board
> > when surrounded by n black pieces in Go.
> >
> >
> > The formula is:
> >
> >
> > a(n) is the integer part of n^2/8 - n/2 + 1.
> >
> >
> > Best regards,
> >
> >
> > Yifan Xie
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

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