A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients

DOI10.1016/j.amc.2013.05.043zbMath1329.11015OpenAlexW2015545432MaRDI QIDQ902533

Necati Taškara, Hasan Hüseyin Güleç, Kemal Uslu

Publication date: 18 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.05.043

zbMATH Keywords

binomial coefficientsFibonacci numberLucas numbergeneralized Fibonacci number

Mathematics Subject Classification ID

Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (14)

A new operational matrix of Caputo fractional derivatives of Fermat polynomials: an application for solving the Bagley-Torvik equation ⋮ THE NUMBER OF SUBSETS OF THE SET CONTAINING NO TWO CONSECUTIVE EVEN INTEGERS ⋮ INFINITE SUMS RELATED TO THE GENERALIZED FIBONACCI NUMBERS ⋮ SOME IDENTITIES OF k-MERSENNE NUMBERS ⋮ Generalized Pascal's triangles and associated \(k\)-Padovan-like sequences ⋮ Further study on the conformable fractional Gauss hypergeometric function ⋮ Connection formulae between generalized Lucas polynomials and some Jacobi polynomials: application to certain types of fourth-order BVPs ⋮ Generalized golden ratios defined by means ⋮ A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications ⋮ Generalized Lucas polynomial sequence approach for fractional differential equations ⋮ New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials ⋮ A generalization of generalized Fibonacci and generalized Pell numbers ⋮ Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials ⋮ New formulas including convolution, connection and radicals formulas of \(k\)-Fibonacci and \(k\)-Lucas polynomials

Cites Work

• On the order-\(m\) generalized Fibonacci \(k\)-numbers
• Fibonacci matrices, a generalization of the ``Cassini formula, and a new coding theory
• A new family of \(k\)-Fibonacci numbers
• On the properties of Lucas numbers with binomial coefficients
• Parametrized Fibonacci search method with \(k\)-Lucas numbers
• Combinatorial sums and finite differences
• The \(k\)-Fibonacci sequence and the Pascal 2-triangle
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