`An Umbral Scheme for Self-Avoding Walks with at most`
` 0 L-R pairs per vertical cross-section is`
            F[2]()   F[3]() (q + 1)
[F[1]() = - ------ - -------------- + F[4](q), F[2]() = 1,
            q - 1        q - 1

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

                 2        2          2
         F[2]() q  x[1] (q  x[1] - 1)
    - -----------------------------------
                   2                    2
      (-1 + q x[1])  (-1 + x[1]) (q - 1)

                    2        2          2
            F[3]() q  x[1] (q  x[1] - 1)
     - 2 -----------------------------------
                      2                    2
         (-1 + q x[1])  (-1 + x[1]) (q - 1)

                2     2               2
       F[4](q) q  x[1]  (-q x[1] + 2 q  - 1)
     - -------------------------------------
                       2
            (-x[1] + q)  (-1 + q x[1])

                   2     2        2        2                 2
       F[4](x[1]) q  x[1]  (q - 1)  (q + 1)    F[4](q) D[1] q  x[1]
     + ------------------------------------- + --------------------], {1}
                       2              2             -x[1] + q
            (-x[1] + q)  (-1 + q x[1])

`The first 60 terms of the enumerating sequence are`
[1, 2, 6, 17, 45, 119, 307, 792, 2014, 5123, 12909, 32538, 81470, 204037, 
508481, 1267424, 3147134, 7815786, 19351586, 47919459, 118369259, 292420612, 
720926746, 1777498365, 4375027183, 10769157521, 26469457991, 65062910070, 
159724276622, 392129982067, 961630639663, 2358334581342, 5778022035784, 
14156945560550, 34656472602978, 84842575695381, 207542898371861, 
507709168604359, 1241139774163211, 3034157529192494, 7412815673860172, 
18110851403508321, 44222902743871067, 107985444615134460, 263546750197686680, 
643218971390803060, 1569110395818938090, 3827860821495439563, 
9334024808307615601, 22760882071503535130]