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

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*In <math>LUCAS(n)</math>, <math>n</math> is the numbers position, which is used to displaying the numbers in the given range. | *In <math>LUCAS(n)</math>, <math>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 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 | + | *The Lucas numbers are defined by: |

− | + | <math>L_n=\begin{cases} 2 &if &n=0 \\ | |

− | + | 1 &if &n=1 \\ | |

− | + | L_{n-1}+L_{n-2} &if &n>1 | |

− | + | \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.... | ||

*The relation between Lucas and Fibonacci numbers are: | *The relation between Lucas and Fibonacci numbers are: |

## Revision as of 17:32, 20 July 2017

**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 numbers.
- 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 and , but and .
- 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:

and : where is the Lucas series with is the Lucas number and is the Fibonacci number.

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

## Related Videos

## See Also

## References