Evaluations of the Hankel determinants of a Thue–Morse-like sequence
Résumé
We obtain simple relations between the Hankel determinants of the formal power series Q k≥0 (1 + Jx 3 k) where J = (√ −3 − 1)/2, and prove that the sequence of Hankel determinants is an aperiodic automatic sequence taking value in {±1, ±J, ±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). It is worth mentioning that we do not have a unified result, even though Bacher's result and ours are very similar.
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