  Circular permutations on {1,2,...,n} that avoid a given pattern correspond to
ordinary (linear) permutations that end with n and avoid all cyclic rotations
of the pattern. Three letter patterns are all but unavoidable in circular
permutations and here we give explicit formulas for the number of circular
permutations that avoid one four letter pattern. In the three essentially
distinct cases, the counts are as follows: the Fibonacci number F_{2n-3} for
the pattern 1324, 2^{n-1}-(n-1) for 1342, and 2^{n}+1-2n-{n}choose{3} for 1234.
