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

Allan Wechsler acwacw at gmail.com
Wed Jun 15 16:34:56 CEST 2022

```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/
>

```