Growth rate of binary words avoiding xxxR

Consider the set of those binary words with no non-empty factors of the form xxxR. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this paper, we demonstrate the existence of upper and lower bounds of the form nlg⁡n+o(lg⁡n) on the number of such words of length n, where lg⁡n denotes the base-2 logarithm of n.