9766
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
A Family of Generalized Fibonacci and Lucas Numbers
This Demonstration displays integer sequences of the form
and
, where
and
are the roots of the quadratic equation
with integer coefficients
and
.
Contributed by:
Abdulrahman Abdulaziz
THINGS TO TRY
Gamepad Controls
SNAPSHOTS
DETAILS
If
and
are integers, then the roots of the quadratic equation
are
and
.
It turns out that
produces a Lucas-like sequence, while
produces a Fibonacci-like sequence. In particular, if
, we obtain the Lucas and Fibonacci numbers.
Reference:
Integer Sequences of the Form a^n + b^n
RELATED LINKS
Fibonacci Number
(
Wolfram
MathWorld
)
Lucas Number
(
Wolfram
MathWorld
)
PERMANENT CITATION
Abdulrahman Abdulaziz
"
A Family of Generalized Fibonacci and Lucas Numbers
"
http://demonstrations.wolfram.com/AFamilyOfGeneralizedFibonacciAndLucasNumbers/
Wolfram Demonstrations Project
Published: June 9, 2010
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Mixed Base Gray Codes
Michael Schreiber
Number Theory Tables
Ed Pegg Jr
Resizable Number Theory Tables
Ed Pegg Jr
Discrete Number Theory Plots
Ed Pegg Jr
Mortal Fibonacci Rabbits
Oleksandr Pavlyk
Fibonacci and Padovan Spiral Identities
Robert Dickau
Bell Number Diagrams
Robert Dickau
Fibonacci Mountain Matra Meru
Michael Schreiber
Look and Say Sequence Steps
Michael Schreiber
Dirichlet's Theorem
Jay Warendorff
Related Topics
Discrete Mathematics
Integers
Number Theory
Sequences
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+