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

[Sean A. Irvine]

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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