[seqfan] Re: Probable mistake in A013582 (number of states in Connect-4).

[Allan Wechsler]

Thank you, Sean. I was sloppily using the word "row" to mean "line" (or,
better, "goal configuration", since knight's-move lines are possible but
don't win). So the answer would have been (c) if I had more carefully
written what I meant.

I still think this is worth saying, at least in the comments.

On Sun, Dec 4, 2022 at 2:22 AM Sean A. Irvine <sairvin at gmail.com> wrote:

> Hi Allan,
>
> The sequence doesn't actually correspond to any of the cases you mention,
> but rather the usual rules of connect 4.  The game ends as soon as any line
> of 4 (horizontal, vertical, or diagonal) first appears or when the board is
> complete without any such line. When the game ends it is possible for the
> last play to result in a line longer than 4 or multiple such lines, kind of
> like your (c), but not restricted to rows.
>
> Sean.
>
>
> On Sun, 4 Dec 2022 at 18:35, Allan Wechsler <acwacw at gmail.com> wrote:
>
> > The entry A013582 <https://oeis.org/A013582> has an ambiguity; it
> doesn't
> > say whether it is including positions that contain (a) *no* winning rows
> of
> > four (that is, only positions that have not yet been won), (b) *at most
> one
> > *row of four (that is, including some winning positions), (c) *any number
> > *of
> > rows of four *as long as they are the same color and intersect in a
> single
> > cell that is at the top of its column *(that is, including all winning
> > positions), or (d) *with any number* of rows of four, unrestricted (that
> > is, including all positions that can be achieved simply by dropping in
> red
> > and blue chips alternately, ignoring winning conditions).
> >
> > These four sequences would definitely be different, and all of
> > approximately equal interest; perhaps the entry should clarify exactly
> what
> > is being counted.
> >
> > On Sat, Dec 3, 2022 at 5:14 PM Russ Cox <rsc at swtch.com> wrote:
> >
> > > Hi Neil, Sean, Sidney,
> > >
> > > I got the sequence very wrong in 1996. (Sorry! I was a high school
> > > student.)
> > > Sean corrected it in 2018 and I wrote an independent program that
> agreed
> > > through a(15).
> > > Looks like Sean computed the later terms.
> > > I can't find my 2018 program at the moment - I should have uploaded it
> > > then.
> > > But I'm sure it was not able to get out to a(42), or I wouldn't have
> > > stopped at a(15).
> > > In any event, I will leave it to Sean and Sidney to work out the right
> > > terms.
> > >
> > > Best,
> > > Russ
> > >
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> > >
> >
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> >
>
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