  Consider the set of those binary words with no non-empty factors of the form
$xxx^R$. 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 on the number of such words of length
$n$, where each of these bounds is asymptotically equivalent to a (different)
function of the form $Cn^{\lg n+c}$, where $C$, $c$ are constants.
