Recently we have been making studies [1, 2] on the Fibonacci number system that appears to be of considerable importance to the Fibonacci computer [3], A specific result that appears to be of particular interest is that through multilevel coefficients on a Fibonacci radix system, efficient extension of representations can occur. For example, through a ternary coefficient system, a doubling of t...

Fibonacenes (zig-zag unbranched catacondensed benzenoid hydrocarbons) are a class of polycyclic conjugated systems whose molecular graphs possess remarkable properties, often related with the Fibonacci numbers. This article is a review of the chemical graph theory of fibonacenes, with emphasis on their Kekulé–structure–related and Clar–structure–related properties. ————————————————— ∗Supported ...

We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.

In this paper, we study the symmetric and generating functions for odd even terms of second-order linear recurrence sequences. introduce a operator in order to derive new family Mersenne numbers, Lucas (p,q)- Fibonacci-like k-Pell polynomials polynomials. By making use defined give some products (p,q)-Fibonacci-like numbers with certain

the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...

The Fibonacci numbers are defined, as usual9 by the recurrence F0 = 0, F1 = 1, Fk = Fk_x +Fk.z, k> 1. The Fibonacci tree of order k, denoted Tk, can be constructed inductively as follows: If k = 0 or k = 1, the tree is simply the root 0. If k > 15 the root is Fk ; the left subtree is Tjc_1; and the right subtree is Tk_2 with all node numbers increased by Fk . TG is shown in Figure 1. For an ele...

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

What are generally referred to as the Fibonacci numbers and the method for their formation were given by Virahanka (between A.D. 600 and X00). Gopala (prior to A.D. 1135) and Hemacandra (c. A.D. 1150). all prior to L. Fibonacci (c. A.D. 1202). Narayana Pandita (A.D. 13Sh) established a relation between his srftcisi~ci-pcrirLfi. which contains Fibonacci numbers as a particular case. and “the mul...

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made about the Fibonacci sequence. It will then go into specific cases of the CRT and how to calculate Fibonacci numbers with reduced forms of the CRT equations. For each of the cases, algorithms and ana...