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Encyclopedia > Fibonacci polynomials

In mathematics, Fibonacci polynomials are a generalization of Fibonacci numbers. These polynomials are defined by:

The first few Fibonacci polynomials are:

The Fibonacci numbers are recovered by evaluating the polynomials at x = 1.


See also


  Results from FactBites:
 
Recursive Sequences (10619 words)
In OEIS: - A001519 a(n) = F(2n-1) = bisection of Fibonacci sequence.
In OEIS: - A001906 F(2n) = bisection of Fibonacci sequence.
In OEIS: - A098127 Fibonacci sequence with a(1)=7 and a(2) = 26.
Fibonacci number - Wikipedia, the free encyclopedia (3020 words)
Fibonacci is also stated as having described the sequence "encoded in the ancestry of a male bee." This turns out to be the Fibonacci sequence.
In music Fibonacci numbers are sometimes used to determine tunings, and, as in visual art, to determine the length or size of content or formal elements.
Fibonacci sequences have been noted to appear in biological settings, such as the branching patterns of leaves in grasses and flowers, branching in bushes and trees, the arrangement of tines on a pine cone, seeds on a raspberry and the like.
  More results at FactBites »


 

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