Consider the challenge of finding the maximum number of pizza pieces (not necessarily slices) one creates with N knife cuts. For example, 0 cuts 1 piece, 1 cut produces 2 pieces, 2 cuts 4 pieces, 3 cuts 7 pieces, 4 cuts 11 pieces, etc. Thus, the sequence is: 1, 2, 4, 7, 11, 16, etc.

Give a dynamic-programming algorithm to compute the n-th number in the sequence. Present the algorithm as a flowchart or pseudocode and explain the main idea behind it.