Résumé
We prove that for any sequence of binary alphabets$\mathcal{A}_1,\mathcal{A}_2,\dots$ , there exists a cube-free word$c_1c_2\dots$so that$c_1\in\mathcal{A}_1,c_2\in\mathcal{A}_2,\dots$ . In particular, for every$n$ , there are at least$1.35^n$cube-free words in$\mathcal{A}_1\times\mathcal{A}_2\times\dots\times \mathcal{A}_n$ . We also prove that if the list of alphabets is computable then one of these words is computable and its$n$ th letter can be computed in time polynomial in$n$ .