  Motivated by multiplication algorithms based on redundant number
representations, we study representations of an integer $n$ as a sum $n=\sum_k
\epsilon_k U_k$, where the digits $\epsilon_k$ are taken from a finite alphabet
$\Sigma$ and $(U_k)_k$ is a linear recurrent sequence of Pisot type with
$U_0=1$. The most prominent example of a base sequence $(U_k)_k$ is the
sequence of Fibonacci numbers. We prove that the representations of minimal
weight $\sum_k|\epsilon_k|$ are recognised by a finite automaton and obtain an
asymptotic formula for the average number of representations of minimal weight.
Furthermore, we relate the maximal order of magnitude of the number of
representations of a given integer to the joint spectral radius of a certain
set of matrices.
