Golden ratio

Methods of Correcting Errors in Messages Encoded by Fibonacci Matrices

The main problems of detection and available methods of correcting errors in encoded messages with Fibonacci matrices, which make it possible to find and correct one, two and three errors in the same or different lines of the code word, are analyzed. It has been found that even in the last decade, many scientists have published a significant number of various publications, each of which to one degree or another substantiates the expediency of using Fibonacci matrices for (de)coding data.

The Formulas for Sum of Products of Sequences Associated With the Metallic Means

In this paper, the regularities of convolution of sequences c of Fibonacci numbers {Fn} generated by metallic means and the sum of products of two statistically independent sequences {Fi} and Jn=j∙sin(0.5π(n-j)) are investigated. It is shown that the known closed forms of sums for convolutionn ... and product ...

On the Universal Regularity of the Numbers of Generalized Recurrence Sequence and Solutions to Its Characteristic Equation of Second Order

In this work shows that the classical oscillations of the ratio of neighboring members of the Fibonacci sequences are valid for arbitrary directions on the plane of the phase coordinates, approaching, to a maximum, the solutions to the characteristic quadratic equation at a given point. The values of the solutions to the characteristic equation along the satellites are asymptotically close to their integer values of the corresponding root lines.