scholarly journals A note on Q-matrices and higher order Fibonacci polynomials

2021 ◽  
Vol 27 (1) ◽  
pp. 91-100
Author(s):  
Paolo Emilio Ricci ◽  
Keyword(s):  
Recent Article ◽  
Representation Formula ◽  
Higher Order ◽  
Fibonacci Polynomials ◽  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences

The results described in a recent article, relative to a representation formula for the generalized Fibonacci sequences in terms of Q-matrices are extended to the case of Fibonacci, Tribonacci and R-bonacci polynomials.

scholarly journals Diophantine Triples and k-Generalized Fibonacci Sequences

2016 ◽  
Vol 41 (3) ◽  
pp. 1449-1465 ◽  
Author(s):  
Clemens Fuchs ◽  
Christoph Hutle ◽  
Florian Luca ◽  
László Szalay
Keyword(s):  
Diophantine Triples ◽  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences

A Small Surrogate for the Golden Angle in Time-Resolved Radial MRI Based on Generalized Fibonacci Sequences

2015 ◽  
Vol 34 (6) ◽  
pp. 1262-1269 ◽  
Author(s):  
Stefan Wundrak ◽  
Jan Paul ◽  
Johannes Ulrici ◽  
Erich Hell ◽  
Volker Rasche
Keyword(s):  
Time Resolved ◽  
Golden Angle ◽  
Radial Mri ◽  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences

Multiplicative Independence in k-Generalized Fibonacci Sequences

2016 ◽  
Vol 56 (4) ◽  
pp. 503-517 ◽  
Author(s):  
Carlos Alexis Gómez Ruiz ◽  
Florian Luca
Keyword(s):  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences

scholarly journals On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 700 ◽  
Author(s):  
Pavel Trojovský
Keyword(s):  
Diophantine Equation ◽  
Fibonacci Sequence ◽  
Generalized Fibonacci Sequence ◽  
Generalized Fibonacci Sequences ◽  
Fibonacci Sequences

The k-generalized Fibonacci sequence ( F n ( k ) ) n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k ≥ 2 , is defined by the values 0 , 0 , … , 0 , 1 of starting k its terms and such way that each term afterwards is the sum of the k preceding terms. This paper is devoted to the proof of the fact that the Diophantine equation F m ( k ) = m t , with t > 1 and m > k + 1 , has only solutions F 12 ( 2 ) = 12 2 and F 9 ( 3 ) = 9 2 .

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