A gray code for a regular language

Given a sequence ${a_m}_{mgeq 0} of strictly increasing positive integers such that $a_0=1$, any non-negative integer $N$ can be uniquely represented by $N=sum_{igeq 0} d_i a_i $, where $d_i$ are non negative integers. The coefficients $d_i$ form a string over a finite alphabet and all these strings form a language having different properties depending on the sequence. We investigate on the possibility of defining a Gray code over the language arising from particular choices of ${a_m}_{mgeq 0}$. We consider the sequence defined by a two termed linear recurrence with constant coefficients having some particular properties.