Results 111 to 120 of about 879,292 (211)

More generalized k(ε)-Fibonacci sequence, series, and its applications

AIP Advances
In this study, we present a generalized higher-order delta operator with the co-efficient of falling factorial and its inverse, both of which allow us to get more generalized k(ε)-Fibonacci sequences along with their sums, a few theorems, and some ...
Rajiniganth P, Aparna T, Ilyas Khan, Suresh K   +3 more
doaj   +1 more source

Some Fibonacci-Related Sequences

The Fibonacci Quarterly
We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the Walnut theorem-prover. We also prove two new results about synchronized sequences.
Benoit Cloitre, Jeffrey Shallit
openaire   +2 more sources

Random Fibonacci Words via Clone Schur Functions

Forum of Mathematics, Sigma
We investigate positivity and probabilistic properties arising from the Young–Fibonacci lattice $\mathbb {YF}$ , a 1-differential poset on words composed of 1’s and 2’s (Fibonacci words) and graded by the sum of the digits.
Leonid Petrov, Jeanne Scott
doaj   +1 more source

On truncated fibonacci sequences

, 2007
We prove some theorems concerning truncated Fibonacci sequences, which are defined below in Section 2. We also state some conjectures concerning the period (mod m) of truncated Fibonacci sequences, where the integer m is greater than or equal to 2.
Oezkan, Engin
core  

Generalized Fibonacci Sequences Generated from a $k$--Fibonacci Sequence

Journal of Mathematics Research, 2012
In this paper we will prove that all $k$--Fibonacci sequence contains generalized Fibonacci sequences and we will indicate the form of obtain them.
openaire   +1 more source

Period Lengths of the Incomplete Fibonacci and Incomplete Lucas Sequences Modulo m

Mathematics
In this paper, we investigate the periodic behavior of incomplete Fibonacci and Lucas numbers modulo a positive integer m. Let L(F,k,m) and L(L,k,m) denote the least positive periods of the incomplete Fibonacci and incomplete Lucas sequences modulo m ...
Nazmiye Yilmaz
doaj   +1 more source

Bi-periodic incomplete Fibonacci sequences [PDF]

In this paper, we define the bi-periodic incomplete Fibonacci sequences, we study some recurrence relations linked to them, some properties of these numbers and their generating functions.
Ramírez, José L.
core  

Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019
The uniqueness of the sum of the elements of finite subsets of the odd oreven indexed Fibonacci and Lucas sequences are proved. Moreover, it is shownthat the odd or even indexed Fibonacci and Lucas sequences are superincreasingsequences.
Alparslan Kargın, Emre Kişi, Halim Özdemir   +2 more
doaj  

On Some Inequalities with Fibonacci Numbers via Weighted Reverse Hölder Inequalities

Annales Mathematicae Silesianae
In this paper, we introduce new inequalities for weighted sums of powers. By utilizing known Fibonacci identities alongside our generalized inequalities, we derive new sequences of inequalities for Fibonacci numbers.
Pribanić Anamarija Perušić
doaj   +1 more source

The p-adic valuation of Lucas sequences

, 2016
Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2 − aX − b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms ...
Sanna, Carlo
core