Pell numbers

Pell numbers are a sequence of integers generated by a specific pattern: each number is the sum of twice the previous number and the one before that. Starting with 0 and 1, the sequence goes 0, 1, 2, 5, 12, 29, and so on. They are linked to solutions of certain quadratic equations and appear in areas like approximation of square roots, continued fractions, and geometric problems involving rectangles. Pell numbers grow rapidly and have interesting mathematical properties, making them useful in number theory and algebra.