Results 1  10
of
2,536
Lucas numbers and generalized Fibonacci sequences
"... > L k+2 \Gamma 3 and prove that k+1 X i=1 L i = L k+3 \Gamma 3: The proof follows the usual pattern: k+1 X i=1 L i = k X i=1 L i + L k+1 = (L k+2 \Gamma 3) + L k+1 (by assumption) = (L k+1 + L k+2 ) \Gamma 3 = L k+3 \Gamma 3: These notes are for the personal use of Math 10 students on ..."
Abstract
 Add to MetaCart
only, and may not be reproduced or distributed further. c fl1995 David Schweizer 7:2 The Fibonacci Numbers Exercise 7.2 Conjecture and prove a closed form for n X<F49.55
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
Abstract

Cited by 1108 (51 self)
 Add to MetaCart
This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
SOME IDENTITIES INVOLVING GENERALIZED GENOCCHI POLYNOMIALS AND GENERALIZED FIBONACCILUCAS SEQUENCES
, 1996
"... the case of BernoulliEuler polynomials of higher order and generalized the results of Toscano. The purpose of this paper is to establish some identities containing generalized Genocchi ..."
Abstract
 Add to MetaCart
the case of BernoulliEuler polynomials of higher order and generalized the results of Toscano. The purpose of this paper is to establish some identities containing generalized Genocchi
Generalized FibonacciLucas Sequences its Properties
 Global Journal of Mathematical Analysis
"... Copyright © 2014 Mamta Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Sequences have been fascinating topic for mathema ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
FibonacciLucas sequence that is defined by the recurrence relation 1 2B B Bn n n , 2n with B0 = 2s, B1 = s. We present some standard identities and determinant identities of generalized FibonacciLucas sequences by Binet’s formula and other simple methods.
DIVISIBILITY BY FIBONACCI AND LUCAS SQUARES
"... In Matijasevic's paper [1] on Hilbert's Tenth Problem, Lemma 17 states that F 2 m divides Fmr if and only if Fm divides r. Here, we extend Lemma 17 to its counterpart in Lucas numbers and generalized Fibonacci numbers and explore divisibility by higher powers. In [2], Matijasevic's Le ..."
Abstract
 Add to MetaCart
In Matijasevic's paper [1] on Hilbert's Tenth Problem, Lemma 17 states that F 2 m divides Fmr if and only if Fm divides r. Here, we extend Lemma 17 to its counterpart in Lucas numbers and generalized Fibonacci numbers and explore divisibility by higher powers. In [2], Matijasevic
MULTISECTION OF THE FIBONACCI CONVOLUTION ARRAY AND GENERALIZED LUCAS SEQUENCE
"... The general problem of multisecting a general sequence rapidly becomes very complicated. In this paper we multisect the convolutions of the Fibonacci sequence and certain generalized Lucas sequences. When we 777sect a sequences we write a generating function for every mth ..."
Abstract
 Add to MetaCart
The general problem of multisecting a general sequence rapidly becomes very complicated. In this paper we multisect the convolutions of the Fibonacci sequence and certain generalized Lucas sequences. When we 777sect a sequences we write a generating function for every mth
On Some Identities for kFibonacci Sequence
"... Copyright © 2014 Paula Catarino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain some identities for kFibonacci numbers by ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Copyright © 2014 Paula Catarino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain some identities for kFibonacci numbers
Some Generalized Fibonacci Polynomials
, 2007
"... We introduce polynomial generalizations of the rFibonacci, rGibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular rmino arrangements. ..."
Abstract
 Add to MetaCart
We introduce polynomial generalizations of the rFibonacci, rGibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular rmino arrangements.
SOME IDENTITIES FOR THE GENERALIZED FIBONACCI AND LUCAS FUNCTIONS
, 1999
"... In this paper, we consider the generalized Fibonacci and Lucas functions, which may be defined by ryX _ pinXOX ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In this paper, we consider the generalized Fibonacci and Lucas functions, which may be defined by ryX _ pinXOX
The Order Of The Fibonacci And Lucas Numbers
"... this paper p (r) denotes the exponent of the highest power of a prime p which divides r and is referred to as the padic order of r. We characterize the padic orders p (Fn ) and p (Ln ), i.e., the exponents of a prime p in the prime power decomposition of Fn and Ln , respectively. The characte ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
attention. The analysis of the periodicity modulo any integer ([3], [11], [14], and [8]) of these numbers helps exploring their divisibility properties (e.g., [9]). The periodic property of the Fibonacci and Lucas numbers has been extensively studied (e.g., [16], [13], [17], and [12]). Here we use some
Results 1  10
of
2,536