Leonardo sequence extension: Tetra-Leonardo, Penta-Leonardo and Hexa-Leonardo

Abstract

This research presents an expansion of the Leonardo sequence, a recurrence associated with a characteristic polynomial of degree 3, now encompassing sequences of recurrences associated with a characteristic polynomial of degree 4 (Tetra-Leonardo), recurrence associated with a characteristic polynomial of degree 5 (Penta-Leonardo) and recurrence associated with a characteristic polynomial of degree 6 (Hexa-Leonardo). Furthermore, the matrix representations and generating functions of these numbers are thoroughly investigated, which represents a significant mathematical contribution to the field of Leonardo sequences. In the context of future work, the aim is to apply these sequences in the context of teaching, enabling more in-depth discussions in initial training courses for Mathematics teachers. This has the potential to enrich pedagogical content and promote a more solid understanding of mathematical sequences among future educators.