# Lucas numbers

The *Lucas numbers ^{}* are a slight variation of Fibonacci numbers

^{}. These numbers follow the same recursion:

$${l}_{n+1}={l}_{n}+{l}_{n-1}$$ |

but having different initial conditions^{}: ${l}_{1}=1,{l}_{2}=3$ leading to the sequence
$1,3,4,7,11,18,29,47,76,123,\mathrm{\dots}$.

Lucas numbers have the following property: ${l}_{n}={f}_{n-1}+{f}_{n+1}$ where ${f}_{n}$ is the ${n}^{th}$ Fibonacci number.

Title | Lucas numbers |
---|---|

Canonical name | LucasNumbers |

Date of creation | 2013-03-22 12:19:58 |

Last modified on | 2013-03-22 12:19:58 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 8 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 11B39 |

Synonym | Lucas sequence |

Related topic | FibonacciSequence |