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 numberss.
• 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 L0=2 and L1=1, but F0=0 and F1=1.
• The Lucas numbers are defined by: $Ln={\begin{cases}2ifn=0\\1ifn=1\\Ln-1+Ln-2ifn>1\end{cases}}$

• 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 $L(n)$ is the nth Lucas number and $Fn$ 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