A helpful starting point is the paper entitled "Fibonacci Series Modulo m by D. D. Wall [3]. With Wall, we let /„ denote the n member of the sequence of integers fQ = a, f1 = b9 ..., where fn + 1 = fn + f n _ r The symbol h(m) will denote the length of the period of the sequence resulting from reducing each /„ modulo w. The basic Fibonacci sequence will be given by uQ = 0, ux = 1, ... and the L...

The m-th Cullen number Cm is a number of the form m2 m + 1 and the m-th Woodall number Wm has the form m2 m − 1. In 2003, Luca and Stănică proved that the largest Fibonacci number in the Cullen sequence is F4 = 3 and that F1 = F2 = 1 are the largest Fibonacci numbers in the Woodall sequence. A generalization of these sequences is defined by Cm,s = ms m+1 and Wm,s = ms m−1, for s > 1. In this pa...

The generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all vertices that contain a given binary word f as a factor; the generalized Lucas cube Qd( ↽Ð f ) is obtained from Qd by removing all the vertices that have a circulation containing f as a factor. In this paper the Wiener index of Qd(1) and the Wiener index of Qd( ↽Ð 1) are expressed as functions of the o...

In this paper, we consider the generalized Fibonacci and Pell Sequences and then show the relationships between the generalized Fibonacci and Pell sequences, and the Hessenberg permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Pell Sequence, fPng ; is de…ned by the recurrence...

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs of cyclic polyphenantrenes. In this paper it is proved that the Wiener index of Fibonacci cubes can be written as the sum of products of four Fibonacci numbers which in turn yields a closed formula f...

A new Fibonacci-type sequence is constructed and for it proved that has a basis with 24 elements.

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...

In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which call ordered numbers. We determine the properties numbers including relations with Leonardo, Fibonacci, and Lucas Symmetric antisymmetric Fibonacci are used in proofs. attain some well-known identities, Binet formula, generating function for these Finally, provide illustrations identities.

In this contribution the robustness of a novel steganographic scheme based on the generalized Fibonacci sequence against Chi-square attacks is investigated. In essence, an image is first represented in a basis defined by a generalized Fibonacci sequence. Then the secret data are inserted by substitution technique into selected bit planes preserving the first order distributions, and finally, th...

BACKGROUND In most phase I oncology trials, it is often stated that the dose increments follow a "modified-Fibonacci sequence". This term, however, is vague. METHODS To better characterize this sequence, we reviewed 81 phase I trials based on this concept. RESULTS Out of 198 phase I oncology trials, 81 (41%) are based on modified-Fibonacci series. Actual incremental ratios varied in a large...