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

[Neil Sloane]

Sean,  you might keep Russ in the loop, since it was his sequence

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com



On Sat, Dec 3, 2022 at 2:51 PM Sean A. Irvine <sairvin at gmail.com> wrote:

> Hi Sidney,
>
> You make a plausible case that my existing value for A013582(42) is wrong.
>
> I'll follow up with you in more detail off the list and we can post back a
> summary later when it is resolved.
>
> Sean.
>
>
> On Sun, 4 Dec 2022 at 04:49, Sidney Cadot <sidney at jigsaw.nl> wrote:
>
> > Hi all,
> >
> > Recently I have completed brute-forcing the game of Connect-4 using a
> > self-written program.
> >
> > OEIS contains two relevant sequences concerning the number of positions
> > after *n* plies:
> >
> > A013582 - total number of positions after *n* plies, up to reflection;
> > A212693 - total number of positions after *n* plies.
> >
> > My solver agrees fully with A212693, and with A013582 on all but the last
> > value. Currently, OEIS says A013582(42) = 1459376098; however, the
> solution
> > I found suggests that this value should be 729688049.
> >
> > Note that this value is precisely half the value currently given in
> A013582
> > on OEIS.
> >
> > It is quite hard to reproduce this calculation (a dedicated computer
> worked
> > for about 6 months to traverse the whole game DAG twice, producing some
> 15
> > TB of data in the process), so another line of reasoning is more useful
> to
> > assess my claim that the currently listed value is not correct.
> >
> > Here is such an argument:
> >
> > In general, we find that 2 * A013582(n) is slightly larger than
> A212693(n).
> > This is to be expected, as most boards by far are not their own mirror
> > image, but some are.
> >
> > In fact, we can calculate the number of horizontally *symmetrical *boards
> > after n plies as 2 * A013582(n) - A212693(n), and the total number of
> > *nonsymmetric
> > *boards as A212693(n) - ( 2 * A013582(n) - A212693(n)) = 2 * (A212693(n)
> -
> > A013582(n)).
> >
> > Assuming both the numbers A212693(42) = 1459332899 and A013582(42) =
> > 1459376098 currently in OEIS are correct, we can calculate the number of
> > non-symmetrical full boards as:
> >
> > 2 * (1459332899 - 1459376098) = -86398
> >
> > The actual number of non-symmetrical full boards cannot, of course, be
> > negative. We can therefore conclude that the assumption that A212693(42)
> > and A013582(42) are both correct must be false. Following my solver, I
> > think that this is because the last value of A013582 as currently listed
> is
> > off by a factor of two.
> >
> > My question to the readers: could you review my argument and if you
> agree,
> > make a correction to A013582?
> >
> > With kind regards,
> >
> >   Sidney Cadot
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>