A Study on Matrix Sequence with Generalized Guglielmo Numbers Components

We know that the diverse applications of matrix sequences in fields such as physics, engineering, architecture, nature, and art. Numerous authors have delved into the study of these matrix sequences in existing literature. In this study, we define and investigate the generalized Guglielmo matrix sequence. For this aim we explore four specific cases of that sequence that are called triangular matrix sequences, Lucas-triangular matrix sequences, oblong matrix sequences, and pentagonal matrix sequences. Next, we present Binet's formulas, generating functions, the summation formulas and some elementary identities for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there always exist some relationship between generalized triangular, Lucas-triangular, oblong and pentagonal matrix sequences.