On doubled and quadrupled Fibonacci type sequences
Abstract
In 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.
Keywords
Fibonacci numbers; Padovan’s numbers; generalized Fibonacci numbers; Narayana’s numbers; generating function; Pascal’s triangle
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Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University Turkey
Wydział Matematyki i Fizyki Stosowanej, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
https://orcid.org/0000-0003-1789-6280
Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Yıldırım University Turkey
Wydział Elektrotechniki i Informatyki, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
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