On some properties of bicomplex Gaussian third-order Jacobsthal numbers

In [7], Kuloğlu and Özkan introduced the bicomplex Gaussian Fibonacci numbers and studied the generating functions and Binet’s formulas related to these numbers. Here, we discuss some unknown properties of generalized third-order Jacobsthal numbers. In this paper, we give some properties of the bicomplex Gaussian third-order Jacobsthal and bicomplex Gaussian modified third-order Jacobsthal numbers and obtain some identities for them. Future studies could explore the application of bicomplex Gaussian numbers to other special third-order sequences, such as tribonacci numbers. Also, we find the matrix representation of both new sequences, these matrices can be used in coding theory and cryptography to create new codes and ciphers.