Generalizations of Some Identities Involving the Fibonacci Numbers
نویسنده
چکیده
منابع مشابه
The 99th Fibonacci Identity
In the book Proofs that Really Count [1], the authors use combinatorial arguments to prove many identities involving Fibonacci numbers, Lucas numbers, and their generalizations. Among these, they derive 91 of the 118 identities mentioned in Vajda’s book [2], leaving 27 identities unaccounted. Eight of these identities, presented later in this paper, have such a similar appearance, the authors r...
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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 کاملA new method for obtaining Fibonacci identities
For the Lucas sequence {Uk(P,Q)} we discuss the identities like the well-known Fibonacci identities. For example, the generalizations of F2k = F 2 k+1 − F 2 k−1 and F2k+1 = F 2 k+1 + F 2 k are PU2k = U 2 k+1 − QU k−1 and U2k+1 = U k+1 − QU k , respectively. We propose a new simple method for obtaining identities involving any recurrences and use it to obtain new identities involving the Fibonac...
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.
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