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) {|Δk(t)np|}n,p≥0 is 2-automatic. Moreover, we prove that the three-dimensional sequence (modulo 2) {|Δk(t)np|}n,p,k≥0 is 2-automatic.