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Generalization of the Distance Fibonacci SequencesYilmaz, Nur SeymaWloch, AndrejOzkan, Engindistance Fibonacci numbersgeneralized Fibonacci numbersnegative integersmatrix generatorsHEISENBERG ALGEBRASNUMBERSMathematics, AppliedMathematicsIn this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators for these sequences and offered a graphical representation to clarify their structure. Furthermore, we demonstrated how these generalizations can be applied to obtain the Padovan and Narayana sequences for specific parameter values.MDPI2024Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/16837https://doi.org/10.3390/axioms13070420enAXIOMSinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/16837