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Topic: Fibonacci polynomials

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Fibonacci number

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	Recursive Sequences
		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.
	www.tanyakhovanova.com /RecursiveSequences/RecursiveSequences.html (10619 words)

	Fibonacci number - Wikipedia, the free encyclopedia
		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.
	en.wikipedia.org /wiki/Fibonacci_number (3020 words)

	Arnold Knopfmacher's Publications
		A Knopfmacher and N Robbins,``On Pell Partitions'', {\it The Fibonacci Quarterly { \bf 42}} (2004), 348--352.
		A Knopfmacher and R Warlimont, ``Counting permutations and polynomials with a restricted factorization pattern'', {\it Australasian J. of Combinatorics {\bf 13}} (1996), 151-162.
		A Knopfmacher and E Manstavicius,``On the largest degree of an irreducible factor of a polynomial in $\F_q[x]$'', {Lietuvos Matematikos Rinkinys {\bf 37}} (1997), 50-60.
	www.wits.ac.za /science/number_theory/apublic.htm (1981 words)

	DR Donald Mills
		Gave a talk on January 12 on polynomial sequences whose coefficients are Fibonacci polynomials at the Joint Mathematics Meetings (January 12-15, San Antonio, TX).
		Delivered an invited talk on polynomial sequences whose coefficients are Fibonacci polynomials at the Integers Conference, University of West Georgia, October 27-30, 2005.
		Gave an invited talk on the existence of primitive polynomials satisyfing certain properties at the University of Pennsylvania on February 20.
	www.math.siu.edu /mills/default1.htm (2058 words)

	Fibonacci Polynomials and Parity Domination in Grid Graphs - Goldwasser, Klostermeyer, Ware (ResearchIndex)
		Fibonacci Polynomials and Parity Domination in Grid Graphs (2002)
		In this paper, the Fibonacci polynomials are studied over GF (2) with particular emphasis on their divisibility properties and their relation to the existence of even dominating sets in grid graphs and properties of a corresponding recurrence.
		A key to proving Theorem 2 is an analysis of the Fibonacci index of a polynomial.
	citeseer.ist.psu.edu /goldwasser02fibonacci.html (527 words)

	Fibonacci Numbers Spelled Out
		So the idea is to assume a generic generating function (2) with coefficients representing the Fibonacci numbers.
		And this is a closed-form expression for the Fibonacci numbers' generating function.
		Well, there is a generic way of expanding a ratio of polynomials into Taylor series around the poles.
	ulcar.uml.edu /~iag/CS/Fibonacci.html (605 words)

	Fibonacci polynomials -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-30)
		Fibonacci polynomials -- Facts, Info, and Encyclopedia article
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, Fibonacci polynomials are a generalization of (A number in the Fibonacci sequence) Fibonacci numbers.
		These (A mathematical expression that is the sum of a number of terms) polynomials are defined by:
	www.absoluteastronomy.com /encyclopedia/f/fi/fibonacci_polynomials.htm (83 words)

	A new class of q-Fibonacci polynomials (ResearchIndex)
		Abstract: We introduce a new q-analogue of the Fibonacci polynomials and derive some of its properties.
		0.3: Orthogonal Polynomials and Combinatorics - Stanton (2000)
		2 Fibonacci polynomials (context) - Cigler - 2003
	citeseer.ist.psu.edu /649769.html (324 words)

	Fibonacci polynomial and the Pascal Triangle
		In mathematics polynomial functions, or polynomials, are an important class of simple and smooth functions.
		The Fibonacci numbers are recovered by evaluating the polynomials at x = 1.
		It is obvious that Pascal`s Triangle structure is built in these relations, which certainly indicates the existing connection between the numbers of Pascal`s Triangle and Fibonacci polynomials.
	milan.milanovic.org /math/english/fibo/fibo5.html (198 words)

	Fibonacci Polynomial Home Page
		The Fibonacci polynomials are defined as f_0 (x) = 0; f_1(x) = 1; f_2(x) = x; and f_i(x) = xf_{i-1}(x) + f_{i-2}(x).
		Fibonacci Polynomials and Parity Domination in Grid Graphs; J. Goldwasser, W. Klostermeyer, and H. Ware,Graphs and Combinatorics, vol.
		Divisibility Properties of Fibonacci Polynomials over GF(2); H. Ware; MS Report, Dept. of Statistics and Computer Science, West Virginia University, August 1997
	www.unf.edu /%7Ewkloster/fib.html (402 words)

	The On-Line Encyclopedia of Integer Sequences
		Triangle of numbers {C(n-k,k), n >= 0, 0<=k<=[ n/2 ]}; or, triangle of coefficients of Fibonacci polynomials.
		C.-K. Lim and K. Lam, The characteristic polynomial of ladder graphs and an annihilating uniqueness theorem, Discr.
		The degree of F(n, x) is floor((n-1)/2) and F(2p, x) = F(p, x) times a polynomial of equal degree which is 1 mod p.
	www.research.att.com /~njas/sequences/A011973 (449 words)

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