Manuals/calci/LUCAS

LUCAS(n)

• $n$ is the number indicating the position.

Description

• This function gives the Lucas series of the numbers.
• Lucas numbers are similar to the Fibonacci numbers.
• It is generated by added the last two numbers in the series.
• In $LUCAS(n)$, $n$ 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 $L_{0}=2$ and $L_{1}=1$, but $F_{0}=0$ and $F_{1}=1$.
• The Lucas numbers are defined by: $L_{n}={\begin{cases}2&if&n=0\\1&if&n=1\\L_{n-1}+L_{n-2}&if&n>1\end{cases}}$

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

$L_{n}=F_{n}+2F_{n-1}$ and : $F_{n}={\frac {L_{n-1}+L_{n+1}}{5}}$ where $L$ is the Lucas series with $L_{n}$ is the $n^{th}$ Lucas number and $F_{n}$ is the $n^{th}$ Fibonacci number.

   This function will, give the result as error when  $n$ is non-numeric 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