In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern x x x^R was intermediate between polynomial and exponential. We now show that the same result holds for the growth of the number of binary words avoiding the pattern x x^R x . Curiously, the analysis for x x^R x is much simpler than that for x x x^R. We derive our results by giving a bijection between the set of binary words avoiding x x^R x and a class of sequences closely related to the class of "strongly unimodal sequences".