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Padovan and Perrin generalized quaternions
(Wiley, 2021) Isbilir, Zehra; Gurses, Nurten
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.
Pell-Padovan generalized quaternions
(Bulgarian Acad Science, 2021) Isbilir, Zehra; Gurses, Nurten
The aim of this article is to introduce Pell-Padovan generalized quaternions. It also derives new properties associated with these and takes into account negative indices. Additionally, it presents generating function, Binet-like formula, Simson formula, matrix representations, and several summation properties.
Pentanacci and Pentanacci-Lucas hybrid numbers
(Taylor & Francis Ltd, 2021) Isbilir, Zehra; Gurses, Nurten
The aim of this study is to introduce the Pentanacci and Pentanacci-Lucas hybrid numbers. Then, some properties with respect to these special numbers and relations between them are obtained. In addition, matrix formulations, generating functions, Binet-like formulas and some summation formulas of them are examined.