Let , F(b[1], b[2], b[3]), be the (unnormalized) weight

 of the range of, [[1, 0, 0, 1, 1], [0, 1, 1, 1, 1], [0, 1, 1, 0, 1]], being ,

    [b[1], b[2], b[3]]

           It satisfies the following pure linear recurrece equations

                         with polynomial coefficients

       F(b[1], b[2], b[3])
-24/7 ----------------------
      2 + b[1] - b[2] + b[3]

           (-13 + 8 b[1] - 8 b[2]) F(b[1] + 1, b[2], b[3])
     + 1/7 -----------------------------------------------
                       2 + b[1] - b[2] + b[3]

     + F(2 + b[1], b[2], b[3]) = 0



      (b[1] - 1 - b[2] + b[3]) F(b[1], b[2] + 1, b[3])
-21/8 ------------------------------------------------
            (b[2] - b[3] + 3) (b[2] - b[3] + 2)

           (8 b[1] - 37 - 8 b[2]) F(b[1], b[2] + 2, b[3])
     - 1/8 ----------------------------------------------
                          b[2] - b[3] + 3

     + F(b[1], 3 + b[2], b[3]) = 0



     (b[2] - b[3]) (b[2] - 1 - b[3]) F(b[1], b[2], b[3])
64/9 --------------------------------------------------- - 1/3
             (b[3] + 2) (2 + b[1] - b[2] + b[3])

    (b[2] - 1 - b[3]) (-8 b[2] + 16 b[3] + 45 + 8 b[1]) F(b[1], b[2], b[3] + 1)

    /((b[3] + 2) (2 + b[1] - b[2] + b[3])) + F(b[1], b[2], b[3] + 2) = 0



            These recurrences enable to compute, in linear time any

                     desired value of , F(b[1], b[2], b[3])

                        subject to the inital conditions

[[[29, 0], [21, 259/2], [0, 147/2]], [[111/2, 0], [87, 1241/4], [63/2, 777/2]]]