The number of binary rotation words.

We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be Theta(n(4)). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [Problemy Kibernet. 39 (1982) 67-84], then independently by Mignosi [Theoret. Comput. Sci. 82 (1991) 71-84], and others.