[seqfan] Re: A002831 incompatible with A002830
njasloane at gmail.com
Tue Sep 9 03:37:21 CEST 2014
Sean, Don't do anything right now. Let me check if I have
a copy of Read's thesis.
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
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