On a conjecture of Deutsch, Sagan, and Wilson
Abstract
We prove a recent conjecture due to Deutsch, Sagan, and Wilson stating that the finite sequence obtained from the first p central trinomial coefficients modulo p by replacing nonzero terms by 1's is palindromic, for any prime number p > 3. Addendum: the result was proved before almost in the same way by Tony D. Noe: On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html
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Cite
@article{arxiv.math/0606670,
title = {On a conjecture of Deutsch, Sagan, and Wilson},
author = {Jean-Paul Allouche},
journal= {arXiv preprint arXiv:math/0606670},
year = {2007}
}
Comments
This conjecture of Deutsch, Sagan, and Wilson has been already proved in Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html