Isbilir, ZehraCurses, Nurten2025-10-112025-10-1120241225-293X2288-6176https://doi.org/10.5831/HMJ.2024.46.3.407https://hdl.handle.net/20.500.12684/21457The purpose of this article is to bring together the Horadam numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and examine a new type of quite big special numbers system, which is called Horadam 3-parameter generalized quaternions (shortly, Horadam 3PGQs), and special cases of them. Besides, we compute both some new equations and classical well-known equations such as; Binet formulas, generating function, exponential generating function, Poisson generating function, sum formulas, Cassini identity, polar representation, and matrix equation. Furthermore, this article concludes by presenting the determinant, characteristic polynomial, characteristic equation, eigenvalues, and eigenvectors in relation to the matrix representation of Horadam 3PGQ.en10.5831/HMJ.2024.46.3.407info:eu-repo/semantics/closedAccessKey words and phrases. Horadam numbers3-parameter generalized quaternionsspecial recurrence sequencesfundamental matrixArticle463407427WOS:001300532500006N/A