On the powers of the k-Fibonacci numbers

被引：0

作者：

Falcon, Sergio ^{[1
,2
]}

机构：

[1] Univ Las Palmas de GC, Dept Math, Las Palmas Gran Canaria, Spain

[2] Univ Las Palmas de GC, Inst Appl Microelect IUMA, Las Palmas Gran Canaria, Spain

来源：

ARS COMBINATORIA | 2016年 / 127卷

关键词：

k-Fibonacci numbers; k-Lucas numbers; Recurrence laws;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we will find a combinatorial formula that relates the power of a k-Fibonacci number, F-k,n(p), to the number F-k,F-a n. From this formula and if p is odd, we will find a new formula that allows to express the k-Fibonacci number F-k,F-(2r+1)n as a combination of odd powers of F-k,F-n. If p is even, the formula is similar but for the even k-Lucas numbers L-k,L-2rn.

引用

页码：329 / 338

页数：10

共 7 条

[1] [Anonymous], 1994, FDN COMPUTER SCI
[2] Deutsch E, 2006, ON LINE ENCY INTEGER
[3] FALCON S., 2011, International Journal of Contemporary Mathematical Sciences, V6, P1039
[4] The k-Fibonacci sequence and the Pascal 2-triangle
Falcon, Sergio
Plaza, Angel
[J]. CHAOS SOLITONS & FRACTALS, 2007, 33 (01) : 38 - 49
[5] On the Fibonacci k-numbers
Falcon, Sergio
Plaza, Angel
[J]. CHAOS SOLITONS & FRACTALS, 2007, 32 (05) : 1615 - 1624
[6] On k-Fibonacci numbers of arithmetic indexes
Falcon, Sergio
Plaza, Angel
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 208 (01) : 180 - 185
[7] Spinadel V. W., 2002, INT MATH J, V2, P279

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