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Revision difference : Lucas numbers |
| Version current |
Version 4 |
| The \emph{Lucas numbers} are a slight variation of Fibonacci numbers. |
The \emph{Lucas numbers} are a slight variation of Fibonacci numbers. |
| These numbers follow the same recursion: |
These numbers follow the same recursion: |
| $$l_{n+1}=l_n + l_{n-1}$$ |
$$l_{n+1}=l_n + l_{n-1}$$ |
| but having different initial conditions: $l_1=1, l_2=3$ leading to the sequence |
but having different initial conditions: $l_1=1, l_2=3$ leading to the sequence |
| $1, 3, 4, 7, 11, 18, 29, 47, 76, 123,\ldots$. |
$1, 3, 4, 7, 11, 18, 29, 47, 76, 123,\ldots$. |
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Lucas numbers have the following property: $l_n=f_{n-1}+f_{n+1}$ where $f_n$ is the $n^{th}$ Fibonacci number.
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Lucas numbers have the following property: $l_n=f_{n-1}+f_{n+1}$ where $f_n$ is the $n$th Fibonacci number.
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