Difference between revisions of "Lucas numbers"
From specialfunctionswiki
| Line 4: | Line 4: | ||
=Properties= | =Properties= | ||
[[Sum of Lucas numbers]]<br /> | [[Sum of Lucas numbers]]<br /> | ||
| + | [[L(n)=F(n+1)+F(n-1)]]<br /> | ||
=See also= | =See also= | ||
Revision as of 00:26, 25 May 2017
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
Sum of Lucas numbers
L(n)=F(n+1)+F(n-1)
See also
References
- S.L. Basin and V.E. Hoggatt, Jr.: A Primer on the Fibonacci Sequence Part I (1963)... (previous)... (next) (specifies the following equivalent initial conditions instead: $L(1)=1$ and $L(2)=3$)
