Padovan and Perrin generalized quaternions

Abstract

In this study, we investigate the Padovan (or Cordonnier) and Perrin generalized quaternions. We obtain the new identities for these special quaternions related to matrix forms. We also introduce Binet-like formulae, generating functions, several summation, and binomial properties concerning these quaternions.

On the Weighted Padovan and Perrin Sums

“…It is well known that the sum of the first n terms for the Padovan and Perrin sequences can be given as follows, respectively, Generalizations and some properties of the Padovan sequence can be found in [7][8][9][10][11]. It is the aim of this paper to explore some of the properties of the third-order sequences of thePadovan and Perrin numbers {} n P and {} n R , respectively, and their weighted sums.…”

On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions

“…. More studies about the quaternions can be found in [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”

Examination of generalized Tribonacci dual quaternions

“…Some properties of Padovan quaternions are studied in [15]. Padovan and Perrin generalized quaternions are determined in [24]. Real quaternions with generalized Tribonacci numbers are examined in [2].…”