[seqfan] R: Number of real roots of polynomial with coefficients +-1, or 0, +-1

Luca Petrone luca.petrone at libero.it
Sun Feb 26 07:21:34 CET 2017


I agree with Chai correction and extended by one term, so far.
I noticed that polynomials with c_0 and c_n of different sign have always same 
or more nonzero real roots than polynomials with  c_0 and c_n of same sign : 
can this be demonstrated ?
Best Regards,
Luca Petrone

>----Messaggio originale----
>Da: "Neil Sloane" <njasloane at gmail.com>
>Data: 26/02/2017 1.08
>A: "Sequence Fanatics Discussion list"<seqfan at list.seqfan.eu>
>Ogg: [seqfan] Re Number of real roots of polynomial with coefficients +-1, or 
0, +-1
>
>OK, I added the third sequence to go along with A282691 and A282692: see
>A282701. I guess this is probably what Oanh had in mind
>when we started this discussion.  I put down a guess for the initial
>entries, hoping that Chai Wah or Edwin or Luca will correct them if
>necessary, and also extend them!
>
>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
>
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