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 g[1] g[5] F(b[1], b[2], b[3]) - -------------------------------------- + (g[2] + g[3]) (b[1] - b[2] + b[3] + 2) (-b[2] g[5] + b[1] g[5] - g[1] g[2] - g[1] g[3] + g[5]) F(1 + b[1], b[2], b[3])/((g[2] + g[3]) (b[1] - b[2] + b[3] + 2)) + F(b[1] + 2, b[2], b[3]) = 0 2 g[4] (b[1] + b[3] - b[2] - 1) (g[2] + g[3]) F(b[1], b[2] + 1, b[3]) - -------------------------------------------------------------------- - g[1] g[5] (b[2] - b[3] + 3) (b[2] - b[3] + 2) (-g[1] g[3] - g[1] g[2] - b[2] g[5] + b[1] g[5] - 2 g[5]) g[4] F(b[1], b[2] + 2, b[3])/((b[2] - b[3] + 3) g[1] g[5]) + F(b[1], b[2] + 3, b[3]) = 0 2 g[5] (-1 + b[2] - b[3]) (-b[3] + b[2]) F(b[1], b[2], b[3]) ----------------------------------------------------------- - 2 g[4] (b[3] + 2) (b[1] - b[2] + b[3] + 2) (-1 + b[2] - b[3]) (-b[2] g[5] + 3 g[5] + g[1] g[2] + g[1] g[3] + 2 g[5] b[3] + b[1] g[5]) F(b[1], b[2], b[3] + 1)/(g[4] (b[3] + 2) (b[1] - b[2] + b[3] + 2)) + 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 [[[g[5] + (g[2] + g[3]) g[1], 0], [(g[2] + g[3]) g[4], (g[2] + g[3]) g[5] + 1/2 %1 g[1]], [0, 1/2 %1 g[4]]], 2 [[g[1] g[5] + 1/2 (g[2] + g[3]) g[1] , 0], [ g[4] g[5] + (g[2] + g[3]) g[1] g[4], 2 2 1/2 g[5] + (g[2] + g[3]) g[1] g[5] + 1/4 %1 g[1] ], 2 [1/2 (g[2] + g[3]) g[4] , (g[2] + g[3]) g[4] g[5] + 1/2 %1 g[1] g[4]]]] 2 %1 := (g[2] + g[3])