A Lucas sequence is a series of numbers similar to the Fibonacci sequence, where each number is the sum of the two preceding ones. The sequence starts with the numbers 2 and 1, leading to the following terms: 2, 1, 3, 4, 7, 11, 18, and so on. Lucas sequences can be defined mathematically as L_n = L_n-1 + L_n-2 , with initial values L_0 = 2 and L_1 = 1 . These sequences have various applications in number theory and are named after the French mathematician François Édouard Anatole Lucas.