Perrin n-Dimensional Relations

This work aims, to perform a complexity in the Perrin sequence, to present the two-dimensional, three-dimensional, and n-dimensional recurrence relations of this sequence. Thus, from the one-dimensional relationship of this sequence, we will discuss the increase of its dimensionality and the insertion of imaginary units in the Perrin sequence, which is a recursive sequence of third order and presents large similarities with the Padovan sequence, differing only its initial values. Moreover, we will present a relationship between the Perrin numbers and the Padovan numbers, which will be used to perform the complexity of this sequence.

Keywords:

n-dimensional relations, Perrin sequence, Three-dimensional relations, Two-dimensional relations,

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