We show that an Artinian O-sequence $h_0,h_1,{cdots},h_{d-1},h_d;=;h_{d-1},h_{d+l};>;h_d$ of codimension 3 is not level when $h_{d-1};=;h_d;=;d + i;and;h{d+1};=;d+(i+1);for;i;=;1,;2,;and;3$, which is a partial answer to the question in [9]. We also introduce an algorithm for finding noncancelable Betti numbers of minimal free resolutions of all possible Artinian O-sequences based on the theorem of Froberg and Laksov in [2].