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

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: $\displaystyle Ln=\begin{cases} 2 if n=0 1 if n=1 Ln-1+Ln-2 if n>1 \end{cases} *The sequence of Lucas numbers is 2,1,3,4,7, 11,18,29,...... *The relation between Lucas and Fibonacci numbers are: Ln=Fn+2Fn-1 and Fn=Ln-1+Ln+1\5 where L is the Lucas series with [itex] L(n)$ 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

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