Results 201 to 210 of about 48,003 (223)

Generalized Fibonacci Number Triples

The American Mathematical Monthly, 1973
(1973). Generalized Fibonacci Number Triples. The American Mathematical Monthly: Vol. 80, No. 2, pp. 187-190.
A. G. Shannon, A. F. Horadam
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Solutions for k -Generalized Fibonacci Numbers Using Fuss-Catalan Numbers

The Fibonacci quarterly
We present new expressions for the $k$-generalized Fibonacci numbers, say $F_k(n)$. They satisfy the recurrence $F_k(n) = F_k(n-1) +\dots+F_k(n-k)$. Explicit expressions for the roots of the auxiliary (or characteristic) polynomial are presented, using ...
S. R. Mane
semanticscholar   +1 more source

A note on generalized Fibonacci numbers

Journal of Discrete Mathematical Sciences and Cryptography, 2001
Abstract Starting from the simplest recurrence relations of second order, in this paper are suggested direct solutions obtained from a generalization of Pascal’s Triangle. With some binomial formulas, it isn’t necessary anymore to calculate roots of associated equations, and the extension of parameters’ definition field to the complex field can be done
Eugeni F, MASCELLA, RAFFAELE
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Identities for generalized fibonacci numbers

International Journal of Mathematical Education in Science and Technology, 2004
This note introduces a family of generalized Fibonacci numbers and provides some identities these numbers satisfy. The results are proved using clever rearrangements, rather than using induction.
L. Monk, D. Tang, D. Brown
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Generalized Fibonacci–Leonardo numbers

Journal of Difference Equations and Applications, 2023
Urszula Bednarz, Małgorzata Wołowiec-Musiał   +1 more
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Generalized Fibonacci numbers and applications

2009 IEEE International Conference on Systems, Man and Cybernetics, 2009
The present paper relates to the methods for data encoding and the reading of coded information represented by colored (including monochrome/black, gray) symbols (bars, triangles, circles, or other symbols). It also introduces new algorithms for generating secure, reliable, and high capacity color barcodes by using so called weighted n-dimensional ...
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Generalized commutative Fibonacci p-number quaternions

Mathematica Applicanda
Summary: The Fibonacci \(p\)-numbers are a generalization of classical Fibonacci numbers, where \(p\) is a non-negative integer. For a Fibonacci \(p\)-number denoted as \(F_p(n)\), starting with initial values \(F_p(1) = F_p(2) = \cdots = F_p(p+1) = 1\). The paper explores generalized commutative quaternions of Fibonacci \(p\)-numbers and some of their
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Reciprocals of Generalized Fibonacci Numbers

The Fibonacci Quarterly, 1971
Shannon, A. G., Horadam, A. F.
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Generalized Fibonacci Number

The Fibonacci Quarterly, 1980
Anne Silva, Verner E. Hoggatt
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Sums of generalized Fibonacci numbers

2008
Let \(\{w_n(a,b;p,q)\}\) be the generalized Fibonacci sequence \[ w_0 = a, w_1 = b, w_n = pw_{n-1} + qw_{n-2} \text{ for } n \geq 2, \] where \(q, b, p, q\) are arbitrary complex numbers and \(q \geq 0\). Explicit formulae of sums \[ \sum_{i=0}^n w_{r+ti}(a,b;p,q),\quad\sum_{i=0}^n (-1)^i w_{r+ti}(a,b;p,q),\quad \sum_{i=0}^n k^i w_{r+ti}(a,b;p,q), \] \[
Cerin Z., GIANELLA, Gian Mario
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