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On a conjecture of Deutsch, Sagan, and Wilson

Jean-Paul Allouche
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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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Jean-Paul Allouche. 2006-10-26. On a conjecture of Deutsch, Sagan, and Wilson. https://arxiv.org/abs/math/0606670

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