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Pell-Lucas Number

Definition

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P = 2 and Q = - 1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to Q_n = F_(n - 1)(2) + F_(n + 1)(2), where F_n(x) is a Fibonacci polynomial. The Pell-Lucas and Pell numbers satisfy the recurrence relation Q_n = 2Q_(n - 1) + Q_(n - 2) with initial conditions Q_0 = Q_1 = 2 for the Pell-Lucas numbers and P_0 = 0 and P_1 = 1 for the Pell numbers.

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Édouard Lucas | John Pell

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