Some Trigonometric Identities Involving Fibonacci and Lucas Numbers
نویسنده
چکیده
In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √
منابع مشابه
Fibonacci Identities and Graph Colorings
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
متن کاملar X iv : 0 80 5 . 09 92 v 1 [ m at h . C O ] 7 M ay 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
متن کاملar X iv : 0 80 5 . 09 92 v 2 [ m at h . C O ] 8 J ul 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
متن کاملIdentities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums
As in [1, 2], for rapid numerical calculations of identities pertaining to Lucas or both Fibonacci and Lucas numbers we present each identity as a binomial sum. 1. Preliminaries The two most well-known linear homogeneous recurrence relations of order two with constant coefficients are those that define Fibonacci and Lucas numbers (or Fibonacci and Lucas sequences). They are defined recursively ...
متن کاملComputational Aspects of Graph Coloring and the Quillen–Suslin Theorem
We generalize both the Fibonacci and Lucas numbers to the context of graphcolorings, and prove some identities involving these numbers. As a corollary we obtain newproofs of some known identities involving Fibonacci numbers such asFr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
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