Evaluations of the Hankel determinants of a Thue–Morse-like sequence
Guo-Niu Han, Wen Sheng Wu · International Journal of Number Theory · 2015
We obtain simple relations between the Hankel determinants of the formal power series ∏k≥0(1 + Jx3k) where [Formula: see text], and prove that the sequence of Hankel determinants is an aperiodic automatic sequence taking value in {±1, ±J, ±J2}. 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.