Senturk, Gulsum Yeliz2024-09-112024-09-1120230354-5180https://doi.org/10.2298/FIL2328753Shttps://hdl.handle.net/11363/8034In this investigation, the aim is to determine a generalized quaternionic sequence with Vietoris' number components depending on 2-parameters & alpha; and 13. Considering specific real values & alpha; and 13, various types of classical quaternionic sequence with Vietoris' number components can be obtained as real, split, split-semi and so on. The fundamental algebraic structures, several classical expressions, a two and three term recurrence relations are identified, as well as Catalan-like, generating function and Binet-like formulas. Furthermore, a determinantal approach is used to generate the generalized quaternionic sequence with Vietoris' number components.eninfo:eu-repo/semantics/openAccessVietoris' number sequencegeneralized quaternionrecurrence relationCatalan's identitygenerating functionBinet's formulaArticle37289753976810.2298/FIL2328753S2-s2.0-85168972672WOS:001052795700001Q2