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Lucas numbers (Definition)

The Lucas numbers are a slight variation of Fibonacci numbers. These numbers follow the same recursion:

\begin{displaymath}l_{n+1}=l_n + l_{n-1}\end{displaymath}

but having different initial conditions: $l_1=1, l_2=3$ leading to the sequence $1, 3, 4, 7, 11, 18, 29, 47, 76, 123,\ldots$.

Lucas numbers have the following property: $l_n=f_{n-1}+f_{n+1}$ where $f_n$ is the $n^{th}$ Fibonacci number.



"Lucas numbers" is owned by Mathprof. [ full author list (2) | owner history (2) ]
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See Also: Fibonacci sequence

Other names:  Lucas sequence
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Cross-references: property, sequence, initial conditions, numbers, Fibonacci numbers, variation
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This is version 5 of Lucas numbers, born on 2002-02-15, modified 2006-09-01.
Object id is 1963, canonical name is LucasNumbers.
Accessed 6354 times total.

Classification:
AMS MSC: 11B39 (Number theory :: Sequences and sets :: Fibonacci and Lucas numbers and polynomials and generalizations)
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