Periods of Leonardo Sequences and Bivariate Gaussian Leonardo Polynomials

In this study, we investigate the periodic characteristics of Leonardo, Leonardo-Lucas, and Gaussian Leonardo sequences, presenting our findings through lemmas and theorems. Additionally, we introduce the concept of the power Leonardo like sequences and characterize the modules and integers within which these sequences exist. Furthermore, we conduct a comparative analysis between these power sequences and the power Fibonacci sequence under the same modulus. Lastly, we define a bivariate Gaussian Leonardo polynomial sequence and obtain specific properties associated with it.