Almost everywhere balanced sequences of complexity 2n + 1

We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The is defined two matrices and we show that it measurably isomorphic to shift on set $\{1,2\}^\mathbb{N}$ of directive sequences. For given $\mathcal{C}$ substitutions, there exists $\mathcal{C}$-adic sequence for every vector letter frequencies or, equivalently, sequence. their factor complexity at most $2n+1$ if only are rationally independent representation primitive. It turns out in this case, dendric. also prove $\mu$-almost balanced, where $\mu$ any shift-invariant ergodic Borel probability measure giving positive cylinder $[12121212]$. second Lyapunov exponent matrix cocycle negative.