Definition:Lucas Number/Definition 2
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Definition
The Lucas numbers are a sequence defined as:
- $L_n = F_{n - 1} + F_{n + 1}$
where $F_k$ is the $k$th Fibonacci number.
Sequence
The Lucas sequence begins:
- $2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, \ldots$
Also see
Source of Name
This entry was named for François Édouard Anatole Lucas.
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-1}$ Principle of Mathematical Induction: Exercise $13$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $11$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $11$