Journal ArticleDOI
A Generalized Fibonacci Sequence
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This article is published in American Mathematical Monthly.The article was published on 1961-05-01. It has received 303 citations till now. The article focuses on the topics: Fibonacci number & Fibonacci word.read more
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On the Fibonacci k-numbers
Sergio Falcon,Ángel Plaza +1 more
TL;DR: In this paper, the authors introduced a general kth Fibonacci sequence that generalizes, between others, both the classic FIFO sequence and the Pell sequence, by studying the recursive application of two geometrical transformations used in the well-known 4TLE partition.
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The k-Fibonacci sequence and the Pascal 2-triangle
Sergio Falcon,Ángel Plaza +1 more
TL;DR: In this paper, the general k-Fibonacci sequence was found by studying the recursive application of two geometrical transformations used in the well-known 4-triangle longest-edge partition.
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The fibonacci numbers-exposed
Dan Kalman,Robert Mena +1 more
TL;DR: The Lucas numbers as discussed by the authors are a close relative of the Fibonacci numbers and have achieved a kind of celebrity status, referred to as the "two shining stars in the vast array of integer sequences".
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On k-Fibonacci sequences and polynomials and their derivatives
Sergio Falcon,Ángel Plaza +1 more
TL;DR: In this paper, the derivatives of k-Fibonacci polynomials are presented in the form of convolution of KF-FBNs and their properties admit a straightforward proof.
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A New Generalization of Fibonacci Sequence & Extended Binet's Formula
Marcia Edson,Omer Yayenie +1 more
TL;DR: In this article, a new generalization {qn }, with initial conditions q 0 = 0 and q 1 = 1, which is generated by the recurrence relation qn = aq n-1 + q n-2 (when n is even) or q n = bq n−1+ q n−2 (When n is odd), where a and b are nonzero real numbers.
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Book
History of the Theory of Numbers
Abstract: THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H. Cresse. Next comes an account of existing knowledge on quadratic forms in three or more variables, followed by chapters on cubic forms, Hermitian and bilinear forms, and modular invariants and covariants.History of the Theory of Numbers.Prof. Leonard Eugene Dickson. Vol. 3: Quadratic and Higher Forms. With a Chapter on the Class Number by G. H. Cresse. (Publication No. 256.) Pp. v + 313. (Washington: Carnegie Institution, 1923.) 3.25 dollars.