The k-Jacobsthal p-sequences and its applications

Abstract

In this paper, we define the k-Jacobsthal p-numbers and then we obtain some properties such as the generating matrix, the Binet formula, the generating function, the exponential representation, the combinatorial representations and the sums. Also, we study the k-Jacobsthal p-numbers modulo m. Furthermore, we define Jacobsthal p-orbit of a finite group and then we obtain the periods of the Jacobsthal p-orbits of the Fox group G(1,4), the polyhedral group (2,3,3) and the dihedral group D_2n. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.