Explicit evaluations of the Hankel determinants of a Thue--Morse-like sequence

Guo-Niu Han; Wen Wu

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arXiv · 1406.1594

Explicit evaluations of the Hankel determinants of a Thue--Morse-like sequence

Guo-Niu Han·Wen Wu

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Abstract

We obtain the explicit evaluations of the Hankel determinants of the formal power series $\prod_{k\geq 0}(1+Jx^{3^{k}})$ where $J={(\sqrt{-3}-1)}/2$, and prove that the sequence of Hankel determinants is an aperiodic automatic sequence taking value in $\{0, \pm 1, \pm J, \pm J^2\}$. This research is essentially inspired by the works about Hankel determinants of Thue--Morse-like sequences by Allouche, Peyrière, Wen and Wen (1998), Bacher (2006) and the first author (2013).

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Guo-Niu Han, Wen Wu. 2014-06-06. Explicit evaluations of the Hankel determinants of a Thue--Morse-like sequence. https://arxiv.org/abs/1406.1594

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