[seqfan] Re: An alternating sequence whose sequence of absolute values appears in the OEIS

[Neil Sloane]

Jack,  That is a sequence which crops up very frequently, and so I think it
would be a good idea to have a second version of it with signs.  So please
go ahead and send it in.

Best regards
Neil

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



On Thu, Feb 11, 2021 at 12:52 AM Jack Grahl <jack.grahl at gmail.com> wrote:

> Dear all,
>
> The sequence g(n) = (-1)^n(3^n -1)/2 is described in the 1973 article 'Some
> polynomials associated with graphs' by Tutte. He defines a graph polynomial
> g(G) and thence a(n) := g(Xn) where Xn is the multigraph with 1 vertex and
> n loops.
>
> This is a fact which I don't think it's covered by any of the numerous
> definitions and remarks on https://oeis.org/A007051 [a(n) = (3^n-1)/2,
> without the alternating signs]. Does it make more sense to add the
> alternating version of the sequence with the formula and this definition?
> Or should I just as a remark to A007051 that this related sequence is
> mentioned in the paper and give the reference?
>
> Thanks for advice. Let me know if anyone wants any more information.
>
> Yours,
> Jack Grahl
>
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