Definition:Lucas Number/Definition 2

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

• Equivalence of Definitions of Lucas Numbers

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): $11$