[seqfan] Re: A002831 incompatible with A002830
Neil Sloane
njasloane at gmail.com
Tue Sep 9 05:25:50 CEST 2014
PS
Sean, What about the case when the nodes are labeled, A006712
and A006713 - can you check them?
Neil
On Mon, Sep 8, 2014 at 11:04 PM, Neil Sloane <njasloane at gmail.com> wrote:
> Sean,
> I found the letter that Ron Read sent me on 4 Feb 1971
> containing A002830, A002831 and a number of other sequences.
> He says all these sequences appeared in his 1958 thesis (which I do not have).
>
> Since most of these sequences were included in the 1973
> Handbook and the 1995 Encyclopedia, Ron's table is worth preserving,
> so I will scan it and put it on the OEIS server and make links to it
> from the relevant sequences.
>
> Concerning A002831, can you correct it and add your new terms?
> In the Extension section, say something like
> a(5) and a(6) corrected and new terms a(7) and a(8) computed by Sean
> A. Irvine, Sep 08 2014.
> I will add a reference to Read's letter and say something about the
> errors. I'm also creating a new entry, A246598, for
> the incorrect values, describing it as an erroneous version of A002831
> (so that if anyone sees it in the two books, they will
> get a pointer to the correct version - that's what we usually do with
> published but incorrect sequences).
>
> Good work, catching these errors from the distant past!
>
> Neil
>
> On Mon, Sep 8, 2014 at 9:37 PM, Neil Sloane <njasloane at gmail.com> wrote:
>> Sean, Don't do anything right now. Let me check if I have
>> a copy of Read's thesis.
>>
>> Neil Sloane
>>
>> On Mon, Sep 8, 2014 at 8:06 PM, Sean A. Irvine <sairvin at xtra.co.nz> wrote:
>>> The terms of A002831 do not match the description:
>>>
>>> A002831: 1, 4, 11, 60, 362, 2987
>>> Computed: 1, 4, 11, 60, 318, 2806, 23445, 314518
>>>
>>> If F(x) is the generating function for A002831, then we have
>>>
>>> G(x) = exp(sum(F(x^k)/k, k=1..infinity))
>>>
>>> is the generating function for A002830. That is, this transform
>>> permits going from a count of connected graphs to the corresponding
>>> count of total graphs (i.e. included disconnected cases). [As an
>>> aside the corresponding inverse is by Mobius inversion
>>> F(x) = sum(mu(k) * log(G(x^k)) / k, k=1..infinity).]
>>>
>>> Applying the g.f. transformation to the "Computed" values yields the
>>> current values for A002830 giving me confidence that the computed
>>> values are correct.
>>>
>>> I don't have access to R. C. Read's dissertation, so I cannot verify
>>> where the existing values for a(5) and a(6) came from.
>>>
>>> Should I update the entry for A002831 (which some comment about the
>>> original terms), or is some other action appropriate?
>>>
>>> Regards,
>>> Sean A. Irvine
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> --
>> Dear Friends, I have now retired from AT&T. New coordinates:
>>
>> Neil J. A. Sloane, President, OEIS Foundation
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
--
Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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