On bicomplex third-order Jacobsthal numbers

Abstract

The aim of this work is to consider the bicomplex third-order Jacobsthal numbers and to present some properties involving this sequence, including the Binet-style formulae and the generating functions. Furthermore, Cassini's identity and d'Ocagne's identity for this type of bicomplex numbers are given, and a different way to find the nth term of this sequence is stated using the determinant of a four-diagonal matrix whose entries are bicomplex third-order Jacobsthal numbers.