The Fibonacci sequence is one of the most beautiful and febulas mathematical concepts. Number turn in place that you have probably seen nature. a series numbers follows unique integers sequence. These generate patterns can be found all real life. are also called golden ratio. section used for architect, art, Space exploration, etc. Keywords: Numbers, Golden ratio

What is the ANZL Algorithm? It is a genuine result of our work which is theoretically and practically proved. By using the ANZL Algorithm, we can test whether a given number belongs to Lucas’s series. It can also be used to find a sequence of Lucas’s numbers, starting from any number . If a given number completes the relation , we can say that it is a Lucas number and we mark it as . From the p...

Abstract: We first study the relationship between the k-Fibonacci numbers and the elements of a subset of Q. Later, and since generally studies that are made on the Fibonacci sequences consider that these numbers are integers, in this article, we study the possibility that the index of the k-Fibonacci number is fractional; concretely, 2n+1 2 . In this way, the k-Fibonacci numbers that we obtain...

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, Fp(n), and their sums, Pn i1⁄41F pðiÞ, and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sum...

In this study, new properties of Fibonacci numbers is given. Also, generalization of some properties of Fibonacci numbers is investigated with binomial coefficiations. Mathematics Subject Classification: 11B39, 11B65

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.