  Dyck paths (also balanced brackets and Dyck words) are among the most heavily
studied Catalan families. This paper is a continuation of [2, 3, 4]. In the
paper we are dealing with the numbering of Dyck paths, with the resulting
numbers, the terms of the OEIS sequence A036991, which encode Dyck paths and
which we have called the Dyck numbers. In this sequence, it turned out to be
promising to investigate nested term patterns. The sequence is constructed
entirely from nested patterns, with each pattern having an infinite number of
copies. We have already considered repeated triplets of adjacent odd numbers;
copies of such triplets in the process of expansion form quite complex
structures, the analysis of which allows us to understand the structure of
A036991. Additionally, we note that the composition of the terms of each
pattern is repeated many times by a simple shift (offset) of Dyck numbers by
some fixed value. As a result, pattern copies give us important parts of most
levels and even give us new levels.
