Generalized Multiple Counting Jacobsthal Sequences of Fermat Pseudoprimes

This study involves definitions of regular and representational multiple-counting Jacobsthal sequences of Carmichael numbers. We introduce recurrence relations for multiple-counting Jacobsthal sequences and show their association with Fermat's little theorem. We also provide matrix representations and generalized I3inet formulas for defined sequences. This leads to a better understanding of how certain composite numbers are distributed among consecutive powers.