Enumerative problems solution for single-transition serial sequences with an adjacent series heights increment bounded from above

In this paper, sets of $n$-valued finite serial sequences are investigated. The sequences consist of two serial subsequences as follows. A sequence begins with an increasing subsequence and ends with a decreasing subsequence or vice versa. The structure of such sequences is determined by restrictions on the number of series, the series lengths, and the series heights.
For sets of sequences, whose difference between heights of the adjacent series does not exceed a certain given value, the algorithms that assign smaller numbers to lexicographically lower sequences and smaller numbers to lexicographically higher sequences have been developed.