[seqfan] A257007 in three different contexts (?)

Neil Sloane njasloane at gmail.com
Thu Nov 26 02:42:46 CET 2015


Dear Sequence Fans:
The sequence https://oeis.org/A257007
just arose in a possibly different context.

The sequence appears to be the same as the function Phi(n)
in Theorem 4 of this paper:
P. Kleban and A. Özlük. A farey fraction spin chain. Communications in
mathematical physics, 203(3):635-647, 1999. Also
http://arxiv.org/pdf/cond-mat/9808182.pdf.

I discovered this when I was looking at a recent thesis:

M. P. Technau, The Calkin-Wilf Tree and a Trace Condition, Master's Thesis,
Julius-Maximilian’s University of Würzburg, Faculty for Mathematics and
Computer Science, 2015;
http://www.mathematik.uni-wuerzburg.de/~steuding/technau.pdf

On page 14 there is a triangle of numbers. The first column
of the triangle seems to match A257007, and the row sums
in the triangle are twice the first column.

I created three new sequences, A264597, A264598, A264599 from this paper.

It would be nice to know for certain that it is the same sequence (A257007)
in all three cases!

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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