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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
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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
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