Some generalized results related to Fibonacci sequence

Some Generalized Fibonacci Polynomials

We introduce polynomial generalizations of the r-Fibonacci, r-Gibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular r-mino arrangements.

Some Asymptotic Properties of Generalized Fibonacci Numbers

1. INTRODUCTION Horadam [1] has generalized two theorems of Subba Rao [3] which deal with some asymptotic p r o p e r t i e s of Fibonacci numbers. Horadam defined a sequence {w (n 2) where a , a are the roots of x 2-P 21 x + P 2 2 = 0. We shall let 06 """ LX r\ r\ UO r\-| • Horadam established two theorems for {w n }: I. The number of terms of {w n } not exceeding N is asymptotic to log(Nd/(P ...

Some Divisibility Properties of Generalized Fibonacci Sequences

Let c be any square-free integer, p any odd prime such that (c/p) = -1, and n any positive integer. The quantity ./IT, which would ordinarily be defined (mod p) as one of the two solutions of the congruence: x E c (mod p n ) , does not exist. Nevertheless, we may deal with objects of the form a + b/c~(mod p), where a and b are integers, in much the same way that we deal with complex numbers, th...

Tenacity and some related results

Conceptually graph vulnerability relates to the study of graphintactness when some of its elements are removed. The motivation forstudying vulnerability measures is derived from design and analysisof networks under hostile environment. Graph tenacity has been anactive area of research since the the concept was introduced in1992. The tenacity T(G) of a graph G is defined asbegin{center} $T(G)=di...

Some Results in Generalized Serstnev Spaces