Difference between revisions of "Lucas numbers"
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(Created page with "The Lucas numbers, $L \colon \mathbb{Z} \rightarrow \mathbb{Z}$, is the solution to the following initial value problem: $$L(n+2)=L(n)+L(n+1), \quad L(0)=2, L(1)=1.$$ =See al...") |
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The Lucas numbers, $L \colon \mathbb{Z} \rightarrow \mathbb{Z}$, is the solution to the following initial value problem: | The Lucas numbers, $L \colon \mathbb{Z} \rightarrow \mathbb{Z}$, is the solution to the following initial value problem: | ||
$$L(n+2)=L(n)+L(n+1), \quad L(0)=2, L(1)=1.$$ | $$L(n+2)=L(n)+L(n+1), \quad L(0)=2, L(1)=1.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Sum of Lucas numbers]]<br /> | ||
=See also= | =See also= | ||
Revision as of 00:17, 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
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 $L(2)=3$)
