An Analytical Approach to Exponent-Restricted Multiple Counting Sequences

Abstract

This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I also studied matrix representations and obtained generalized Binet formulas for defined sequences. As a result of multiple-counting sequence explanation, this study leads to a better understanding for distribution of composite numbers between consecutive bases.