Titlebook: Applications of Fibonacci Numbers; Volume 6 Proceedings Gerald E. Bergum,Andreas N. Philippou,Alwyn F. Hor Conference proceedings 1996 Kluw

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2074v Alpha1-Beta1 and Alpha6-Beta1-Integrin0 < α < 1, be irrational, let x = x(α) be the infinite string whose n-th element is “c” or “d” depending on whether [(n + l)α] − [na] equals 0 or 1 respectively, with [z] denoting the greatest integer function. For integer . ≥ 0 define .., .. by. with L(s) denoting the length of the string s.

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Subwords of the Golden Sequence and the Fibonacci Words,= ., w. = b, w. = w and each w. equals w.w.. w.w., ... The basic structure and properties of Fibonacci words have been studied in [2–6]. In this paper, we determine all the prefixes of Fibonacci words and the subwords of the golden sequence that are of Fibonacci lengths.

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Interesting Arrays Associated with Fibonacci Sequences,different integers in the set when increased by some fixed integer n is a perfect square. Several of these articles have even examined the possibility of finding a set of four or more positive rational numbers with the same property.

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The Zeckendorf Decomposition of Certain Classes of Integers,t use of .. instead of .., such a representation is . [1] and is commonly referred to as the . of . (ZD of ., in brief). Since the ZD of a class of integers is in general unpredictable, its discovery is always a pleasant surprise to the researcher. This fact led us to undertake this kind of investigations.

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Rooks on Fibonacci Boards,ards ..(.). These start with a p-gon C. for odd ., and a vertex point C. for even ., and then are surrounded by [n/2] complete coronas .. of neighbor cells. The boards B.(p,q) and B.(q, p) are dual. The self dual boards ..(4,4) are the well known . x .-square boards or chessboards.

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,Hofstadter’s Conjecture for ,,0 < α < 1, be irrational, let x = x(α) be the infinite string whose n-th element is “c” or “d” depending on whether [(n + l)α] − [na] equals 0 or 1 respectively, with [z] denoting the greatest integer function. For integer . ≥ 0 define .., .. by. with L(s) denoting the length of the string s.

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Abundance of Degrees of Freedomdifferent integers in the set when increased by some fixed integer n is a perfect square. Several of these articles have even examined the possibility of finding a set of four or more positive rational numbers with the same property.