Padovan and Perrin generalized quaternions - Isbilir, Zehra; Gurses, Nurten (WILEY, 2022)
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.
Keywords: Binet-like formulae; binomial sums; generalized quaternions; generating functions; Padovan numbers; Perrin numbers; Mathematics