On a new improved unifying closed formula for all Fibonacci-type sequences and some applications

被引：2

作者：

Kaddoura, Issam ^{[1
]}

Mourad, Bassam ^{[2
]}

机构：

[1] Lebanese Int Univ, Fac Arts & Sci, Dept Math, Saida, Lebanon

[2] Lebanese Univ, Dept Math, Fac Sci, Beirut, Lebanon

来源：

JOURNAL OF NUMBER THEORY | 2018年 / 182卷

关键词：

Generalized Fibonacci sequence; Fibonacci number; Lucas number; Pell sequence; Pell-Lucas sequence; Chebychev polynomial; Fibonacci polynomial; Lucas polynomial; Jacobsthal polynomial; Jacobsthal-Lucas polynomial; Lucas-Lehmer test; LUCAS; PROOF;

D O I：

10.1016/j.jnt.2017.06.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a new general framework under which all generalized Fibonacci-type sequences come together. The main result lies in obtaining one new general closed formula solution for all such sequences by using only matrix theory. This new formula in turn gives new closed formula solutions for most well-known sequences of this type. Next, the advantages of this formula are exploited. In particular, two applications are presented; one deals with finding the most general congruence formula for such sequences which generalizes most known formulas of this type and the other is concerned with computational number theory. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：271 / 283

页数：13

共 50 条

[21] THE HYPERBOLIC-TYPE k-FIBONACCI SEQUENCES AND THEIR APPLICATIONS
Tas, Sait
THERMAL SCIENCE, 2022, 26 (SpecialIssue2): : S551 - S558
[22] THE HYPERBOLIC-TYPE k-FIBONACCI SEQUENCES AND THEIR APPLICATIONS
Tas, Sait
THERMAL SCIENCE, 2022, 26 : S551 - S558
[23] The complex-type k-Fibonacci sequences and their applications
Deveci, Omur
Shannon, Anthony G.
COMMUNICATIONS IN ALGEBRA, 2021, 49 (03) : 1352 - 1367
[24] Longest success and failure runs and new polynomials related to the Fibonacci-type polynomials of order k
Antzoulakos, DL
Philippou, AN
APPLICATIONS OF FIBONACCI NUMBERS, VOL 7, 1998, : 29 - 38
[25] SOLUTIONS TO DIOPHANTINE EQUATION X2+XY-Y2=+D, OR NUMBER OF FIBONACCI-TYPE SEQUENCES WITH A GIVEN CHARACTERISTIC
PETERSON, B
HOGGATT, VE
FIBONACCI QUARTERLY, 1975, 13 (03): : 243 - 251
[26] Combined 3-Fibonacci sequences from a new type
Atanassov, Krassimir T.
Shannon, Anthony G.
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2016, 22 (03) : 5 - 8
[27] A local Steiner–type formula for general closed sets and applications
Daniel Hug
Günter Last
Wolfgang Weil
Mathematische Zeitschrift, 2004, 246 : 237 - 272
[28] SOME CONDITIONS FOR ALL-OR-NONE DIVISIBILITY OF A CLASS OF FIBONACCI-LIKE SEQUENCES
PLA, J
FIBONACCI QUARTERLY, 1995, 33 (05): : 464 - 465
[29] A local Steiner-type formula for general closed sets and applications
Hug, D
Last, G
Weil, W
MATHEMATISCHE ZEITSCHRIFT, 2004, 246 (1-2) : 237 - 272
[30] Some results on circulant and skew circulant type matrices with k-Fibonacci sequences
Zhang, Ying
7TH INTERNATIONAL CONFERENCE ON APPLIED PHYSICS AND MATHEMATICS (ICAPM 2017), 2017, 814

← 1 2 3 4 5 →