Abstract
We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the numbernwe give a sequence of identities for them. Moreover, we give matrix generators for distance Fibonacci numbers and their direct formulas.
Highlights
We introduce new types of distance Fibonacci numbers which are closely related with number decompositions
The nth Fibonacci numbers Fn are defined by recurrence relation Fn = Fn−1+Fn−2, n ≥ 2 with the initial conditions F0 = F1 = 1
In this paper we study special decompositions of a number n which are closely related to distance Fibonacci numbers Fd(i)(k, n), for i = 1, 2, 3
Summary
Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35-959 Rzeszow, Poland. Received 2 June 2014; Revised 21 August 2014; Accepted 23 August 2014; Published 23 October 2014. We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the number n we give a sequence of identities for them. We give matrix generators for distance Fibonacci numbers and their direct formulas
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