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Lucas sequence
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Lucas sequence

mathematics
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Quick Summary

The Lucas sequence is a series of numbers defined by a recursive relation, similar to the Fibonacci sequence. Each number in the Lucas sequence is the sum of the two preceding numbers. The sequence begins with 1 and 3, so the next number is 1 + 3 = 4, followed by 3 + 4 = 7, and so on. The sequence progresses as 1, 3, 4, 7, 11, 18, and continues infinitely.1

The Lucas sequence shares the same recursive formula as the Fibonacci sequence: (x_n = x_{n-1} + x_{n-2}). This mathematical concept is related to the golden ratio, a proportion found in nature and art.12

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2 Britannica Sources
  1. Fibonacci sequence
  2. number game - Fibonacci numbers

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