[seqfan] Re: A002831 incompatible with A002830

[Sean A. Irvine]

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/