Bitim, Bahar DemirtürkTopal, Nazım2022-02-152022-02-1520191582-3067https://hdl.handle.net/20.500.14034/154In this paper, we derive some combinatorial properties of generalized Fibonacci quaternion Q(n) and generalized Lucas quaternion K-n, where the components of Q(n) and K-n are generalized Fibonacci number U-n and generalized Lucas number V-n, respectively. Firstly, we obtain some basic identities and use them to prove Catalan identity for Q(n) and K-n. Then we find some sum formulas Sigma(n)(i=0)Qmi+r, Sigma(n)(i=0)Kmi+r, Sigma(n)(i=0)((n)(i))p(i) q(n-i)Q(i) and Sigma(n)(i=0)((n)(i))p(i) q(n-i)K(i) in terms of Q(n) and K-n. Moreover, we derive the generating functions of these generalized quaternions.eninfo:eu-repo/semantics/closedAccessgeneralized Fibonacci numbersgeneralized Lucas numbersgeneralized quaternionsgenerating functionsArticle212239247Q4WOS:0004756724000082-s2.0-85072381997Q4