# Closed formula for Lucas numbers [duplicate]

How do I go about obtaining a closed formula for Lucas numbers?

The Lucas numbers $L_n$ are defined by $L_1 = 1$, $L_2 = 3$, and $L_n = L_{n-1} + L_{n-2}$.

I tried looking into it on my discrete math textbook but I'm really confused. Maybe someone can lay out the steps for it?

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## marked as duplicate by Gerry Myerson, Guess who it is., Aryabhata, anon, HenryApr 20 '12 at 6:40

mystycs: The questions are the same. The conditions $L_{n+2}=L_{n+1}+L_n$ and $L_n=L_{n-1} + L_{n-2}$ (with appropriate range for $n$'s\$) are equivalent. If you still think that there is a difference, could you explain what difference is there? –  Martin Sleziak Apr 20 '12 at 6:28