[seqfan] Re: A002831 incompatible with A002830
njasloane at gmail.com
Tue Sep 9 05:04:34 CEST 2014
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!
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?
>> 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
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