Abstract
We prove a number of conjectures recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence. Furthermore, we study the regularity of sequences involved in the paper, and prove that for all q≥2, the sequence consisting of the positive integers whose odd part is of the form 4k+1 is not q-regular. Finally we establish the 2-regularity of two sequences of Hankel determinants.
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