Recalculation, numbering and generation of serial sequences with detached natural series

The sets of integer-valued serial sequences of the length $m$, whose structure is determined by limitations on the quantity, total length and permitted lengths of natural series, as well as on lengths of separating 0-series are considered. The cases when lengths of boundary series may not satisfy the given constraints are considered as well. Exact solutions to problems of recalculation, coding and generation are obtained for such sets.