Some Trigonometric Identities Involving Fibonacci and Lucas Numbers

被引：0

作者：

Bibak, Kh. ^{[1
]}

Haghighi, M. H. Shirdareh ^{[1
]}

机构：

[1] Shiraz Univ, Dept Math, Shiraz 71454, Iran

来源：

JOURNAL OF INTEGER SEQUENCES | 2009年 / 12卷 / 08期

关键词：

Fibonacci numbers; Lucas numbers; spanning tree; trigonometric identity;

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, using the number of spanning trees in some classes of graphs, we prove the identities: F-n = 2(n-1)/n root Pi (n-1)(k=1) (1-cos k pi/n cos 3k pi/n), n >= 2, Pi(n-1)(k=0) (1+4sin(2) k pi/n) = L-2n-2 = F2n + 2 -F2n-2 -2, n >= 1, where F-n and L-n denote the Fibonacci and Lucas numbers, respectively. Also, we give a new proof for the identity: F-n = Pi([n-1/2])(k=1)(1+4sin(2) k pi/n) = Pi([n-1/2])(k=1) (1+4 cos(2) k pi/n), n >= 4.

引用

页数：5

共 12 条

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