  In this paper, we find an explicit formula for the generating function that
counts the circular permutations of length n avoiding the pattern 23 4 1 whose
enumeration was raised as an open problem by Rupert Li. This then completes in
all cases the enumeration of circular permutations that avoid a single vincular
pattern of length four containing one vinculum. To establish our results, we
introduce three auxiliary arrays which when taken together refine the
cardinality of the class of permutations in question. Rewriting the recurrences
of these arrays in terms of generating functions leads to functional equations
which are solved by various means including the kernel method and iteration.
