Enumeration problems of sets of increasing and decreasing $n$-valued serial sequences with double-ended constraints on series heights

Enumeration problems for $n$-valued serial sequences are considered. Sets of increasing and decreasing sequences whose structure is specified by constraints on lengths of series and on a difference in heights of the neighboring series in the case when this difference lies between $\delta_1$ and $\delta_2$ are examined.
Formulas for powers of these sets and algorithms for the direct and reverse numerations (assigning smaller numbers to the lexicographically lower-order sequences or smaller numbers to the lexicographically higher-order sequences) are obtained.