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