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

[Sidney Cadot]

Great. I have uploaded a corrected b-file and made an edit to reflect the
corrected value.

Thanks, Sidney

On Sun, Dec 4, 2022 at 12:15 AM Sean A. Irvine <sairvin at gmail.com> wrote:

> 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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