Difference between revisions of "Manuals/calci/LUCAS"

Revision as of 23:46, 3 February 2014

LUCAS(n)

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 $L_{0}=2$ and $L_{1}=1$ , but $F_{0}=0$ and $F_{1}=1$ .
The Lucas numbers are defined by: $L_{n}={\begin{cases}2ifn&=0\\1ifn&=1\\L_{n-1}+L_{n-2}ifn&>1\end{cases}}$

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 nth Lucas number and $F_{n}$ is the nth Fibonacci number.

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

@@ Line 8: / Line 8: @@
 *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 <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>L_n=\begin{cases}  2           if  n=0 \\
+*The Lucas numbers  are defined by: <math>L_n=\begin{cases}  2           if  n&=0 \\
-           if  n=1 \\
+           if  n&=1 \\
-                                                             L_{n-1}+L_{n-2}   if  n>1
+                                                             L_{n-1}+L_{n-2}   if  n&>1
                                                \end{cases}</math>