There are More Than 2**(n/17) n-Letter Ternary Square-Free Words
  We prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ... $, improving on Brinkhuis and Brandenburg's lower bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. This is the first improvement since 1983. 
Doron Zeilberger (Temple University)