A sequence of vectors {x(t)} with dimensionNis given, such thatx(t+1) is obtained fromx(t) by introducingpnew elements, deletingpold ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Npoperations and memory locations, in contrast to the conventional way which requires proportional-to-N2operations and memory locations. A non-symmetric case is also treated.