LucasL

The nth Lucas number: the Fibonacci-style recurrence started from , , closely related to Fibonacci.

WikipediaLucas number↗MathWorldLucasNumber↗WikidataQ2503280↗OEISA000032↗Wolfram LanguageLucasL✓↗

LucasL(n)the nth Lucas number .

SageMathlucas_number2(n, 1, -1)↗SymPylucas(n)↗

Domain: Sequences

Details

• Defined by the same recurrence as Fibonacci, , but started from , .
• Closed form: , where and .
• Related to Fibonacci by and, conversely, .
• Consecutive ratios converge to the golden ratio, just as they do for Fibonacci.
• Extends to negative n via .
• compute-engine only accepts a single integer index (no threading over a list, no complex ).

Examples

See also: Fibonacci