A SHORT PROOF FOR A DETERMINANTAL FORMULA FOR GENERALIZED FIBONACCI NUMBERS

被引：5

作者：

Andelic, Milica ^{[1
]}

Da Fonseca, Carlos M. ^{[2
,3
]}

机构：

[1] Kuwait Univ, Dept Math, Safat 13060, Kuwait

[2] Kuwait Coll Sci & Technol, Block 4,POB 27235, Safat 13133, Kuwait

[3] Univ Primorska, FAMNIT, Glagoljsaska 8, Koper 6000, Slovenia

来源：

MATEMATICHE | 2019年 / 74卷 / 02期

关键词：

Fibonacci numbers; Chebyshev polynomials of second kind; determinant;

D O I：

10.4418/2019.74.2.9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this note is to provide a short and elegant proof for a recent determinantal formula for generalized Fibonacci numbers. The attractiveness of the proof presented here is its elementary nature.

引用

页码：363 / 367

页数：5

共 50 条

[1] RETRACTION: DENYING A SHORT PROOF OF A DETERMINANTAL FORMULA FOR GENERALIZED FIBONACCI POLYNOMIALS (Retraction of Vol 11, Pg 52, 2020)
Qi, Feng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS, 2020, 11 (06): : 37 - 37
[2] FORMULA FOR FIBONACCI NUMBERS FROM A NEW APPROACH TO GENERALIZED FIBONACCI NUMBERS
BERNSTEIN, L
[J]. FIBONACCI QUARTERLY, 1976, 14 (04): : 358 - 368
[3] A combinatoric proof and generalization of Ferguson's formula for k-generalized Fibonacci numbers
Kessler, D
Schiff, J
[J]. FIBONACCI QUARTERLY, 2004, 42 (03): : 266 - 273
[4] The Binet formula for the k-generalized Fibonacci numbers
Yang, Sheng-liang
Zhang, Hui-ting
[J]. ARS COMBINATORIA, 2014, 116 : 193 - 204
[5] RETRACTED: DENYING A SHORT PROOF OF A DETERMINANTAL FORMULA FOR GENERALIZED FIBONACCI POLYNOMIALS (Retracted article. See vol. 11, pg. 37, 2020)
Qi, Feng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS, 2020, 11 (01): : 52 - 57
[6] ON A DETERMINANTAL FORMULA FOR DERANGEMENT NUMBERS
Anoelic, Milica
da Fonseca, Carlos m.
[J]. KRAGUJEVAC JOURNAL OF MATHEMATICS, 2023, 47 (06): : 847 - 850
[7] A short proof of the explicit formula for Bernoulli numbers
Rzadkowski, G
[J]. AMERICAN MATHEMATICAL MONTHLY, 2004, 111 (05): : 432 - 434
[8] The Binet formula and representations of k-generalized Fibonacci numbers
Lee, GY
Lee, SG
Kim, JS
Shin, HK
[J]. FIBONACCI QUARTERLY, 2001, 39 (02): : 158 - 164
[9] A Simplified Binet Formula for k-Generalized Fibonacci Numbers
Dresden, Gregory P. B.
Du, Zhaohui
[J]. JOURNAL OF INTEGER SEQUENCES, 2014, 17 (04)
[10] The Binet formula, sums and representations of generalized Fibonacci p-numbers
Kilic, Emrah
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2008, 29 (03) : 701 - 711

← 1 2 3 4 5 →