Results 21 to 30 of about 976 (217)
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
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Mathematics, 2022 The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z.
Waleed Mohamed Abd-Elhameed +2 more
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On dual hyperbolic generalized Fibonacci numbers [PDF]
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
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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
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Generalized Hybrid Fibonacci and Lucas p-numbers [PDF]
, 2022 The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers.
Kocer, E. Gokcen, Alsan, Huriye
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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
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On generalized Fibonacci numbers [PDF]
Applied Mathematical Sciences, 2015 We provide a formula for the $n^{th}$ term of the $k$-generalized Fibonacci-like number sequence using the $k$-generalized Fibonacci number or $k$-nacci number, and by utilizing the newly derived formula, we show that the limit of the ratio of successive terms of the sequence tends to a root of the equation $x + x^{-k} = 2$.
Bacani, Jerico B. +1 more
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Some properties of k-generalized fibonacci numbers [PDF]
, 2021 In the present paper, we propose some properties of the new family K-generalized Fibonacci numbers which related to generalized Fibonacci numbers. Moreover, we give some identities involving binomial coefficients for K-generalized Fibonacci numbers ...
Aydoğdu, A., Özkan, E., Yılmaz, N.
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Notes on generalized and extended Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon +2 more
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“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials
Journal of Physics: Conference Series, 2022 AbstractMany researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields. There are many useful identities on recurrence relation sequence but there main problem to find any term of recurrence ...
Mannu Arya, Vipin Verma
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