On Product Difference Fibonacci Identities

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چکیده

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منابع مشابه

Compositions and Fibonacci Identities

We study formulas for Fibonacci numbers as sums over compositions. The Fibonacci number Fn+1 is the number of compositions of n with parts 1 and 2. Compositions with parts 1 and 2 form a free monoid under concatenation, and our formulas arise from free submonoids of this free monoid.

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Fibonacci numbers and trigonometric identities

Webb & Parberry proved in 1969 a startling trigonometric identity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.

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Random Approaches to Fibonacci Identities

Many combinatorialists live by Mach’s words, and take it as a personal challenge. For example, nearly all of the Fibonacci identities in [5] and [6] have been explained by counting arguments [1, 2, 3]. Among the holdouts are those involving infinite sums and irrational quantities. However, by adopting a probabilistic viewpoint, many of the remaining identities can be explained combinatorially. ...

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ژورنال

عنوان ژورنال: Integers

سال: 2011

ISSN: 1867-0652

DOI: 10.1515/integ.2011.010