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oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/112972026-10-18T20:39:17Zopenairedrivercom_ebyu_10000col_ebyu_10001

ON DOUBLED AND QUADRUPLED FIBONACCI TYPE SEQUENCESYilmaz, Nur ŞeymaWłoch, AndrzejÖzkan, EnginStrzałka, DominikFibonacci numbersgeneralized Fibonacci numbersgenerating functionNarayana’s numbersPadovan’s numbersPascal’s triangleIn this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle. ©2023 The Author(s).Sciendo2024Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/11297https://doi.org/10.2478/amsil-2023-00200860-2107enAnnales Mathematicae Silesianaeinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/11297