Results 11 to 20 of about 1,056,912 (212)
Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]
Notes on Number Theory and Discrete MathematicsWe will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma, Richard Vernon, Gurdial Arora
doaj +4 more sources
The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence
Hittite Journal of Science and Engineering, 2016 In this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are ...
Ahmet Daşdemir
doaj +5 more sources
The generalized Binet formula for $k$-bonacci numbers [PDF]
Elemente der Mathematik, 2023 We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
Harold R. Parks, Dean C. Wills
semanticscholar +3 more sources
Algorithm for Constructing an Analogue of the Binet Formula [PDF]
Programming and Computer Software, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. I. Kuzovatov +2 more
semanticscholar +6 more sources
Extending generalized Fibonacci sequences and their binet-type formula [PDF]
Advances in Difference Equations, 2006 We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence.
Saeki Osamu, Rachidi Mustapha
doaj +4 more sources
THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-$k$ PELL NUMBERS [PDF]
Taiwanese Journal of Mathematics, 2006 In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the
Emrah Kılıç, Dursun Taşçı
semanticscholar +6 more sources
A Unified Explicit Binet Formula for 3rd-Order Linear Recurrence Relations
Advances in Analysis and Applied MathematicsIn this paper, third order generalized linear recurrence relation Vn (aj , pj) = p1Vn−1 + p2Vn−2 + p3Vn−3, p3 ≠ 0, is studied to generate a generalized Tribonacci sequence, where pj , Vj = aj are arbitrary integers.
K. L. Verma
semanticscholar +4 more sources
Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods
Mathematical Journal of Interdisciplinary Sciences, 2019 The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We
Gautam S. Hathiwala, Devbhadra V. Shah
semanticscholar +4 more sources
On the explicit Binet formula of the generalized ${{2}^{nd}}$ orders Recursive relation
Journal of Universal MathematicsIn this paper, second-order generalized linear recurrence relations of the form ${{V}_{n}}\left( {p}_{1},{p}_{2}, {V}_{1},{V}_{2}\right)={{p}_{1}}{{V}_{n-1}}+{p}_{2}{{V}_{n-2}}$ , where ${{p}_{1}},{{p}_{2}},$ ${{V}_{1}}\left( =a \right)$ and $ {{V}_{2 ...
K. L. Verma
semanticscholar +4 more sources
The Binet formula, sums and representations of generalized Fibonacci
European Journal of Combinatorics, 2007 The generalized Fibonacci sequence \({F_p(n)}\) are defined by the following equation for \(n>p+1\) \[ F_p(n)=F_p(n-1)+F_p(n-p-1), \] with initial conditions \[ F_p(1)=F_p(2)=\cdots=F_p(p)=F_p(p+1)=1. \] For \(p=1\), this is the usual Fibonacci sequence.
Emrah Kılıç
semanticscholar +5 more sources