The complex-type k-Fibonacci sequences and their applications
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DOI: 10.1080/00927872.2020.1834573
Abstract: Abstract In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain miscellaneous properties of the complex-type k-Fibonacci numbers… read more here.
Keywords: fibonacci sequences; fibonacci numbers; complex type; type fibonacci ... See more keywords
Iterated Partial Sums of the k-Fibonacci Sequences
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DOI: 10.3390/axioms11100542
Abstract: In this paper, we find the sequence of partial sums of the k-Fibonacci sequence, say, Sk,n=∑j=1nFk,j, and then we find the sequence of partial sums of this new sequence, Sk,n2)=∑j=1nSk,j, and so on. The iterated… read more here.
Keywords: fibonacci numbers; sequence; sums fibonacci; iterated partial ... See more keywords
The Metallic Ratio of Pulsating Fibonacci Sequences
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DOI: 10.3390/sym14061204
Abstract: The golden ratio and the Fibonacci sequence (Fn) are well known, as is the fact that the ratio Fn+1Fn converges to the golden ratio for sufficiently large n. In this paper, we investigate the metallic… read more here.
Keywords: fibonacci; metallic ratio; pulsating fibonacci; ratio ... See more keywords