  We study infinite words u over an alphabet A satisfying the property
  P : P(n)+ P(n+1) = 1+ #A for any n in N, where P(n) denotes the number of
palindromic factors of length n occurring in the language of u. We study also
infinite words satisfying a stronger property PE: every palindrome of u has
exactly one palindromic extension in u. For binary words, the properties P and
PE coincide and these properties characterize Sturmian words, i.e., words with
the complexity C(n)=n+1 for any n in N. In this paper, we focus on ternary
infinite words with the language closed under reversal. For such words u, we
prove that if C(n)=2n+1 for any n in N, then u satisfies the property P and
moreover u is rich in palindromes. Also a sufficient condition for the property
PE is given. We construct a word demonstrating that P on a ternary alphabet
does not imply PE.
