In 2000, Viswanath showed that random Fibonacci sequences grow exponentially and calculated the rate at which they grow assuming the coin flipped was fair. In this paper, we explore the Fibonacci sequences generated by finite, repeating sequences of pluses and minuses. The main results of this paper will be to show the necessary conditions for a sequence to be periodic, as well as to show all t...

We first generalize an identity involving the generalized Fibonacci numbers and then apply it to establish some general identities concerning special sums. We also give a sufficient condition on a generalized Fibonacci sequence {Un} such that Un is divisible by an arbitrary prime r for some 2 < n ≤ r − 2. 1. Preliminaries The generalized Fibonacci and Lucas numbers are defined, respectively, by...

In this paper, we consider the relationships between the sums of the Fibonacci and Lucas numbers and 1-factors of bipartite graphs. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n > 2 Fn = Fn 1 + Fn 2 where F1 = F2 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n > 2 Ln = Ln 1 + Ln 2 where L1 = 1; L2 = 3: The permanent of an ...

It is shown that there are no non-trivial fifth-, seventh-, eleventh-, thirteenthor seventeenth powers in the Fibonacci sequence. For eleventh, thirteenthand seventeenth powers an alternative (to the usual exhaustive check of products of powers of fundamental units) method is used to overcome the problem of having a large number of independent units and relatively high bounds on their exponents...

This paper describes how a subclass of the rational knots* may be constructed sequentially., the knots in the sequence having 19 29 ..., i s ... crossings. For these knots, the values of a certain knot invariant are Fibonacci numbers, the i knot in the sequence having invariant number Fi . The knot invariant has a wide number of interpretations and properties, and some of these will be outlined...

A linear feedback shift register (LFSR) is the basic element of pseudo-random generators used to generate a sequence values for stream cipher. It consists several cells; each cell flip-flop and function. The function polynomial function; this has degree equal number cells in register. elements are connected other two different ways, either Fibonacci mode or Galois mode. In work, we propose real...

In 1858, Stern introduced an array, later called the diatomic array. The array is formed by taking two values a and b for the first row, and each succeeding row is formed from the previous by inserting c+d between two consecutive terms with values c, d. This array has many interesting properties, such as the largest value in a row of the diatomic array is the (r + 2)-th Fibonacci number, occurr...

In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn} . Also, we investigate relationships between generalized Fibonacci and Lucas sequences.

In this paper, an efficient Fibonacci series based hierarchical protocolHFTM (Hierarchical Fibonacci Tree Multicast) is proposed for applicationlayer multicast. It adopts the idea of layer and cluster to construct multicast group members into a hierarchical architecture. During the cluster formation, it considers the underlying network properties to reduce packet delivering on costly links. In ...

In this work, we propose a CODEC design for the forbidden transition free crosstalk avoidance CODEC. Our mapping and coding scheme is based on the binary number system. In this paper we investigate and propose a bus forbidden transition free CODECs for reducing bus delay and our experimental results shows that the proposed CODEC complexity is orders of magnitude better compared to the existing ...