The (ordinary) generating function

          whose coeff. of z^n tells you the number of permutations of

         length n avoiding the set of patterns, {[1, 2, 3], [1, 3, 2]}

                                     equals

                                2
                              -----
                               \
                                )   g[i](1, 1, z)
                               /
                              -----
                              i = 1

              where the vector of formal power series of length, 2

                        in the variables, x[1], x[2], z

                           is the unique vector that

             satisfies the following system of functional equations

g[1](x[1], x[2], z) =

                        2
     2          2   x[2]  g[2](x[1], 1, x[2])   x[2] g[2](x[1] x[2], 1, 1)
    z  x[1] x[2]  + ------------------------- - --------------------------
                            x[2] - 1                     x[2] - 1

                       2          2   x[2] x[1] g[1](x[1], x[2], 1)
g[2](x[1], x[2], z) = z  x[1] x[2]  + -----------------------------
                                                x[1] - 1

       x[2] x[1] g[1](1, x[2], 1)   x[2] x[1] g[2](x[1] x[2], 1, 1)
     - -------------------------- + -------------------------------
                x[1] - 1                       x[1] - 1

       x[2] x[1] g[2](x[2], 1, 1)
     - --------------------------
                x[1] - 1

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