[seqfan] Re: [Seqfan] A sequence related to Go
Neil Sloane
njasloane at gmail.com
Mon Jun 20 17:51:37 CEST 2022
Remember the rule: always leave off the first few terms when looking up a
sequence in the OEIS to see if it is new.
Your sequence IS A001971, as Allan Wechsler has pointed out.
Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com
On Mon, Jun 20, 2022 at 2:41 AM Yifan Xie <xieyifan4013 at 163.com> wrote:
> 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
> > >
> > > --
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> > >
> >
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> >
>
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