# Difference between revisions of "Manuals/calci/LUCAS"

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*It is generated by added the last two numbers in the series. | *It is generated by added the last two numbers in the series. | ||

*In <math>LUCAS(n), n </math> is the numbers position, which is used to displaying the numbers in the given range. | *In <math>LUCAS(n), n </math> is the numbers position, which is used to displaying the numbers in the given range. | ||

− | *The difference between Lucas and Fibonacci numbers are with the first two terms | + | *The difference between Lucas and Fibonacci numbers are with the first two terms <math>L_0=2</math> and <math>L_1=1 </math>, but <math>F_0=0</math> and <math>F_1=1</math>. |

− | *The Lucas numbers are defined by: <math> | + | *The Lucas numbers are defined by: <math>L_n=\begin{cases} 2 if n=0 \\ |

− | + | 1 if n=1 \\ | |

− | + | L_{n-1}+L_{n-2} if n>1 | |

\end{cases}</math> | \end{cases}</math> | ||

*The sequence of Lucas numbers is 2,1,3,4,7, 11,18,29,...... | *The sequence of Lucas numbers is 2,1,3,4,7, 11,18,29,...... | ||

− | *The relation between Lucas and Fibonacci numbers are: | + | *The relation between Lucas and Fibonacci numbers are: <math> L_n=F_n+2F_{n-1} </math> and <math> F_n=\frac{L_{n-1}+L_{n+1}}{5}</math> |

− | where L is the Lucas series with <math> | + | where L is the Lucas series with <math> L_n</math> is the nth Lucas number and <math> F_n </math> is the nth Fibonacci number. |

This function will give the result as error when n is nonnumeric or n < 0 | This function will give the result as error when n is nonnumeric or n < 0 | ||

## Revision as of 04:15, 1 February 2014

**LUCAS(n)**

- is the number indicating the position.

## Description

- This function gives the Lucas series of the numbers.
- Lucas numbers are similar to the Fibonacci numberss.
- It is generated by added the last two numbers in the series.
- In is the numbers position, which is used to displaying the numbers in the given range.
- The difference between Lucas and Fibonacci numbers are with the first two terms and , but and .
- The Lucas numbers are defined by:

- The sequence of Lucas numbers is 2,1,3,4,7, 11,18,29,......
- The relation between Lucas and Fibonacci numbers are: and

where L is the Lucas series with is the nth Lucas number and is the nth Fibonacci number.

This function will give the result as error when n is nonnumeric or n < 0

## Examples

- =LUCAS(5)= 2 1 3 4 7 11
- =LUCAS(0)= 2
- =LUCAS(1)= 2 1
- =LUCAS(3)= 2 1 3 4
- =LUCAS(-1)=Null