[seqfan] Re: A002831 incompatible with A002830

[Neil Sloane]

OK, good! In the mean time then I'll add a note to A2831 saying you
are going to make some corrections soon!

On Tue, Sep 9, 2014 at 1:28 AM, Sean A. Irvine <sairvin at gmail.com> wrote:
> Neil,
>
> I will make the changes as suggested. Might take a day or so, since I
> need to redo my calculation of a(7) and a(8) because of an error in my
> call to nauty.
>
> Sean.
>
> On Tue, Sep 9, 2014 at 3:25 PM, Neil Sloane <njasloane at gmail.com> wrote:
>> 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
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> 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