Codimensions of algebras and growth functions

Let $A$ be an algebra over a field $F$ of characteristic zero and let $c_n(A),\ n=1,2,\ldots,$ be its sequence of codimensions. We prove that if $c_n(A)$ is exponentially bounded, its exponential growth can be any real number $>1$. This is achieved by constructing, for any real number $\alpha >1$, an $F$-algebra $A_\alpha$ such that $\lim_{n\to \infty} \root n \of {c_n(A_\alpha)}$ exists and equals $\alpha$. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.