  This article investigates integer sequences that partition the sequence into
blocks of various lengths - irregular arrays. The main result of the article is
explicit formulas for numbering of irregular arrays. A generalization of Cantor
diagonal method is proposed. We also define and describe intra-block
permutations of natural numbers. Generalizations of reluctant sequences are
introduced, namely generalized reluctant sequences and generalized reverse
reluctant sequences. Explicit formulas are presented for these sequences. The
article provides numerous examples to illustrate all statements.

Combinatorics