Results 1 to 10 of about 351 (163)

A Method to Construct Generalized Fibonacci Sequences [PDF]

Journal of Applied Mathematics, 2016
The main purpose of this paper is to study the convergence properties of Generalized Fibonacci Sequences and the series of partial sums associated with them.
Adalberto García-Máynez, Adolfo Pimienta Acosta   +1 more
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Hidden time-patterns in cyclic human movements: a matter of temporal Fibonacci sequence generation and harmonization [PDF]

Frontiers in Human Neuroscience
Fibonacci sequences are sequences of numbers whose first two elements are 0, 1, and such that, starting from the third number, every element of the sequence is the sum of the previous two.
Cristiano Maria Verrelli, Lucio Caprioli, Marco Iosa, Marco Iosa   +3 more
doaj   +2 more sources

Alternating generalized Fibonacci sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In a recent paper, K.~T. Atanassov and A.~G. Shannon introduced a Fibonacci-like sequence derived from the generalized Fibonacci sequence by incorporating alternating signs into the recurrence relation.
Carlos M. da Fonseca, Paulo Saraiva
doaj   +2 more sources

Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences

Mathematics, 2020
In this paper we consider a generalized bi-periodic Fibonacci {fn} and a generalized bi-periodic Lucas sequence {qn} which are respectively defined by f0=0, f1=1, fn=afn−1+cfn−2 (n is even) or fn=bfn−1+cfn−2 (n is odd), and q0=2d, q1=ad, qn=bqn−1+cqn−2 ...
Younseok Choo
doaj   +3 more sources

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, Peter J.-S. Shiue, Shen C. Huang   +2 more
doaj   +1 more source

The sequence of trifurcating Fibonacci numbers

Ratio Mathematica, 2021
One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’.
Parimalkumar A. Patel, Dr. Devbhadra V. Shah   +1 more
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On a generalization of the Pell sequence [PDF]

Mathematica Bohemica, 2021
The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$.
Jhon J. Bravo, Jose L. Herrera, Florian Luca   +2 more
doaj   +1 more source

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

Mathematics, 2023
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
doaj   +1 more source

LINEARLIZATION OF GENERALIZED FIBONACCI SEQUENCES [PDF]

Korean Journal of Mathematics, 2014
Summary: In this paper, we give linearization of generalized Fibonacci sequences \(\{g_n\}\) and \(\{q_n\}\), respectively, defined by Gupta et al. and Edson et al. and use this result to give the matrix form of the \(n\)-th power of a companion matrix of \(\{g_n\}\) and \(\{q_n\}\). Then we re-prove the Cassini's identity for \(\{g_n\}\) and \(\{q_n\}\
Jang, Young Ho, Jun, Sang Pyo
openaire   +2 more sources

On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source