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

[Sean A. Irvine]

Hi Sidney,

Great news, you are indeed correct.  It looks like I simply forgot to
divide by 2 in the last entry!

I found the outputs from my runs. It looks like what I actually did was
generate all symmetric configurations (or perhaps those that could lead to
symmetric configurations). The timestamps on those files indicate that it
was run 1 Oct 2018 to 3 Oct 2018. So "only" a couple of days to generate
all the data because it was a much smaller set of states needed.  Then I
computed A013582 from the known numbers for A212693 and the count of
symmetric cases.

 The file for n=42 contains 43199 lines (matching the s(n) number in the
table I sent before).  I should have computed (1459332899+43199)/2 =
729688049, but it seems I simply forgot to divide by 2.  When I mailed you
earlier, I was looking at s(n) and thinking it all looked reasonable, but I
did not think to check that I had done the arithmetic step right.

Please go ahead and propose a correction in the OEIS (I or another editor
can then approve).

Sean.

On Sun, 4 Dec 2022 at 09:20, Neil Sloane <njasloane at gmail.com> wrote:

> 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/
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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