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

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*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 L0=2 and L1=1, but F0=0 and F1=1. | *The difference between Lucas and Fibonacci numbers are with the first two terms L0=2 and L1=1, but F0=0 and F1=1. | ||

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

− | 1 if n=1 | + | 1 if n=1\\ |

Ln-1+Ln-2 if n>1 | Ln-1+Ln-2 if n>1 | ||

− | \end{cases} | + | \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,...... | ||

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where L is the Lucas series with <math> L(n)</math> is the nth Lucas number and <math> Fn </math> is the nth Fibonacci number. | where L is the Lucas series with <math> L(n)</math> is the nth Lucas number and <math> Fn </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 | ||

− | |||

==Examples== | ==Examples== |

## Revision as of 04:10, 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 L0=2 and L1=1, but F0=0 and F1=1.
- 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: Ln=Fn+2Fn-1 and Fn=Ln-1+Ln+1\5

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