This is a sample example for SymUGJ

                This is a simple example of an Umbral Scheme for

           for generating functions for enumerating words in {1,2,3}

                       that avoid  any factor of the form

                      1^(a+1)2^(a+1)3^(a+1) , for all a>=0

              and its five permutations, in other words you can't

          have 3 consecutive blocks of all 3 letters of the same length

                              The Umbral Scheme is

                     3                   2        4
                    t              F[1](t  x[1]) t  x[1]
[F[1](x[1]) = - ----------- + 2 ----------------------------
                     3            2                  3
                1 - t  x[1]     (t  x[1] - 1) (-1 + t  x[1])

                           2
                  F[1](1) t
     - 2 ---------------------------- - F[1](t x[1]) t], [6]
           2                  3
         (t  x[1] - 1) (-1 + t  x[1])

              Using this Umbral Scheme, the first 30 terms of the

                            generating function are

[1, 3, 9, 21, 51, 123, 291, 681, 1599, 3753, 8799, 20631, 48363, 113373, 265791,

    623103, 1460769, 3424569, 8028393, 18821415, 44124129, 103442697, 242506653,

    568522251, 1332819249, 3124604547, 7325189409, 17172861033, 40259321709,

    94382233551, 221265675429]

               The whole thing took, 5.400, minutes of CPU time