Some observations on the Rueppel sequence and associated Hankel determinants
P Barry - arXiv preprint arXiv:2005.04066, 2020 - arxiv.org
arXiv preprint arXiv:2005.04066, 2020•arxiv.org
Starting with a definition based on the Catalan numbers, we carry out an empirical study of
the Rueppel sequence. We use the Hankel transform as the main technique. By means of
this transform we find links to such sequences as the Jacobi sequence and the paper-folding
sequence. We also study several number arrays defined by this sequence, which are
analogs of the important Catalan triangles of combinatorics. We identify a sequence related
to the Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the Hankel …
the Rueppel sequence. We use the Hankel transform as the main technique. By means of
this transform we find links to such sequences as the Jacobi sequence and the paper-folding
sequence. We also study several number arrays defined by this sequence, which are
analogs of the important Catalan triangles of combinatorics. We identify a sequence related
to the Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the Hankel …
Starting with a definition based on the Catalan numbers, we carry out an empirical study of the Rueppel sequence. We use the Hankel transform as the main technique. By means of this transform we find links to such sequences as the Jacobi sequence and the paper-folding sequence. We also study several number arrays defined by this sequence, which are analogs of the important Catalan triangles of combinatorics. We identify a sequence related to the Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the Hankel transforms of the paper with classical sequences. Examples are given where certain privileged permutations appearing in the Leibnitz formula for determinants have a special role.
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