Lucas numbers

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The Lucas numbers, $L \colon \mathbb{Z} \rightarrow \mathbb{Z}$, is the solution to the following initial value problem: $$L(n+2)=L(n)+L(n+1), \quad L(0)=2, L(1)=1.$$

Properties[edit]

Sum of Lucas numbers
Sum of Lucas numbers
L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)
L(-n)=(-1)^nL(n)

Relationship to Fibonacci numbers[edit]

L(n)=F(n+1)+F(n-1)
L(n)^2-5F(n)^2=4(-1)^n
F(2n)=F(n)L(n)
L(n)=F(n+1)+F(n-1)

See also[edit]

Fibonacci numbers

References[edit]