I need tp devise an O(n) divide and conquer algorithm to compute the
maximum subsequence sum of a list. The maximum subsequence sum of a
list containing a0, a1, a2...an-1 is the subsequence ai, ai+1, ...aj
such that the sum of these elements is maximum amongst all possible
subsequences. Notice that if all the ak are negative, then the empty
subsequence has the maximum sum of 0.

Say, for example, if A=[-10,2,4,-10,3,4,5,-5,7,-1], then
MaxSubsequenceSum.maxSubsequenceSum(A, 10) returns 14, corresponding
to the subsequence (3,4,5,-5,7).

In pseudo basic, the logic is:

1) maxValue=0
   maxSize=0
   maxIndex=0

2) loop through all array elements. If all values are <=0, then stop and return 0

3) loop through all 0 to n-1 array elements again
   at each index k, 
     array sumof[k,0]= value of array A[k]
     if value of array sumof[k,0] > maxValue then {
        maxValue= value of array A[k]
        maxSize= 0
        maxIndex= k
      }
     loop through elements (k+1) to (n-1)
       at each index m,
          array sumof[k, m-k]=value of array sumof[k, m-k-1] + value of array A[m]
          if value of array sumof[k, m-k] > MaxValue then {
             maxValue = value of array sumof[k, m-k]
             maxSize= m-k
             maxIndex= k
          }
     end loop
   end loop
Return maxValue (although maxSize gives you number-1 of elements in
the array and maxIndex gives you starting element)

This is a free comment.