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Selected Article

In mathematics, the Pell numbers and companion Pell numbers are both sequences of integers that have been known since ancient times. They are defined by a recurrence relation similar to that for the Fibonacci numbers, and grow exponentially, proportionally to powers of the silver ratio. Pell numbers arise in the approximation of the square root of 2, in the definition of square triangular numbers, in the construction of nearly-isosceles integer right triangles, and in certain combinatorial enumeration problems.

As with Pell's equation, the name of the Pell numbers stems from Leonhard Euler's mistaken attribution of the equation and the numbers derived from it to John Pell. The Pell-Lucas numbers are also named after Edouard Lucas, who studied sequences defined by recurrences of this type; the Pell and companion Pell numbers are Lucas sequences.