Automaticity of the Hankel determinants of difference sequences of the Thue–Morse sequence.

Extending the result of Allouche et al., we prove that for any k , the two-dimensional sequence (modulo 2) { | Δ k ( t ) n p | } n , p ≥ 0 is 2-automatic. Moreover, we prove that the three-dimensional sequence (modulo 2) { | Δ k ( t ) n p | } n , p , k ≥ 0 is 2-automatic. [ABSTRACT FROM AUTHOR]