Results 11 to 20 of about 973 (216)
Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences [PDF]
Kyungpook mathematical journal, 2017 In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, $m$ and derive certain interesting properties related to them.
Laugier, Alexandre, Saikia, Manjil P.
openaire +4 more sources
On The Generalized Gaussian Fibonacci Numbers.
Ars Comb., 2017 Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence. In this article firstly we define and study the generalized Gaussian Fibonacci numbers and then find the matrix representation ...
Lee, G.Y., Aşçı, Mustafa
openaire +5 more sources
Carlitz’s Equations on Generalized Fibonacci Numbers
Symmetry, 2022 Carlitz solved some Diophantine equations on Fibonacci or Lucas numbers. We extend his results to the sequence of generalized Fibonacci and Lucas numbers. In this paper, we solve the Diophantine equations of the form An1⋯Ank=Bm1⋯BmrCt1⋯Cts, where (An), (Bm), and (Ct) are generalized Fibonacci or Lucas numbers.
Min Wang, Peng Yang 0019, Yining Yang
openaire +2 more sources
On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers
Advances in Research, 2019 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers and ...
Yüksel Soykan, Soykan, Yüksel
openaire +4 more sources
Advances in Research, 2020 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers and ...
Soykan, Y¨uksel, Y¨uksel Soykan
openaire +4 more sources
Generalized Fibonacci numbers and Blackwell’s renewal theorem [PDF]
Statistics & Probability Letters, 2012 We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.
Christensen, Sören +2 more
openaire +4 more sources
On dual hyperbolic generalized Fibonacci numbers
Indian Journal of Pure and Applied Mathematics, 2019 In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's
Yüksel Soykan
openaire +5 more sources
Restricted Binary Strings and Generalized Fibonacci Numbers [PDF]
, 2017 We provide some interesting relations involving k-generalized Fibonacci numbers between the set \(F_n^{(k)}\) of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding \(k+1\) consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection.
Bernini, Antonio, Antonio Bernini
openaire +4 more sources
Generalized sums of Fibonacci and Lucas Numbers [PDF]
, 2021 Here we are proposing generalized sums for Fibonacci and Lucas numbers. In the case of the Fibonacci sequence, the generalized sum contains four Fibonacci numbers.
Sparavigna, Amelia Carolina +1 more
core +1 more source
Solutions of equations x2−(p2q2±3p)y2=±kt
Examples and Counterexamples, 2022 In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
doaj +1 more source