In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore,  new sequences have been used in order  to introduce a  new class of series. All properties of the se...

In the paper, the authors find a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

Hypergeometric functions are an important tool in many branches of pure and applied mathematics, and they encompass most special functions, including the Chebyshev polynomials. There are also well-known connections between Chebyshev polynomials and sequences of numbers and polynomials related to Fibonacci numbers. However, to my knowledge and with one small exception, direct connections between...

The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number > 2n−1 + 5 have diameter ≤ 4 and determine the order of these trees with respect to their Fibonacci numbers. Furthermore, it is shown that the average Fibonacci number of a star-like ...

In this paper, we consider the relationships between the sums of the generalized order-k Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction We consider the generalized order k Fibonacci and Lucas numbers. In [1], Er de…ned k sequences of the generalized order k Fibonacci numbers as shown: g n = k X j=1 g n j ; for n > 0 and 1 i k; (1.1) with boundary conditions for 1...

In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties these polynomials—among others, a graph interpretation matrix generators. Moreover, present connections with Pascal’s triangle.