A combinatorial approach to the Perrin polynomial sequence and its generalization

The present work approaches the study of a combinatorial interpretation for the Perrin polynomial sequence, aiming at a contribution to the Mathematics teaching area. In view of studies focused on the History of Mathematics containing the teaching of recurring numerical sequences present in textbooks, there is an interest in carrying out a combinatorial approach for a sequence considered to be a cousin of the Fibonacci sequence, which is the Perrin sequence. In this way, we have the definition of Perrin’s polynomial bracelets, investigating Perrin’s polynomial combinatorial model. Finally, combinatorial interpretations for the Perrin polynomial sequence extensions are discussed, generalizing the Perrin polynomial combinatorial model.