Here's a problem I'm trying to solve in order to solve a larger
problem.  Its problem 15.2-4 from the CLRS algorithms text book. 
Define R(i,j) to be the number of times that table entry m[i, j] is
referenced while computing other entries in a call of MatrixChainOrder
(the bottom-up dynamic programming version). Show that the summation
from i = 1 to n of the summation of j = 1 to n of R(i,j) = (n cubed -
n) over 3.