Affiliation:
1. Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Yildirim University, Erzincan, Turkey
Abstract
In this paper, we define five parameters generalization of Fibonacci numbers
that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana,
Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and
Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci
numbers, generalized (k, r)-Fibonacci numbers in the distance sense by
extending the definition of a distance in the recurrence relation with two
parameters and adding three parameters in the definition of this distance,
simultaneously. Tiling and combinatorial interpretations of generalized
Fibonacci numbers are presented, and explicit formulas that allow us to
calculate the nth number are given. Also generating functions and some
identities for these numbers are obtained.
Publisher
National Library of Serbia
Subject
Renewable Energy, Sustainability and the Environment
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