1. On Doubled and Quadrupled Fibonacci Type Sequences
- Author
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Yilmaz Nur Şeyma, Włoch Andrzej, Özkan Engin, and Strzałka Dominik
- Subjects
fibonacci numbers ,padovan’s numbers ,generalized fibonacci numbers ,narayana’s numbers ,generating function ,pascal’s triangle ,11b39 ,11b37 ,11c20 ,Mathematics ,QA1-939 - 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.
- Published
- 2024
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