Lucas Sequence
In mathematics, the Lucas sequences Un(P,Q) and Vn(P,Q) are certain integer sequences that satisfy the recurrence relation
- xn = P xn−1 − Q xn−2
where P and Q are fixed integers. Any other sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences Un(P,Q) and Vn(P,Q).
More generally, Lucas sequences Un(P,Q) and Vn(P,Q) represent sequences of polynomials in P and Q with integer coefficients.
Famous examples of Lucas sequences include the Fibonacci numbers, Mersenne numbers, Pell numbers, Lucas numbers, Jacobsthal numbers, and a superset of Fermat numbers. Lucas sequences are named after the French mathematician Édouard Lucas.
Read more about Lucas Sequence: Recurrence Relations, Examples, Algebraic Relations, Other Relations, Specific Names, Applications
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—Martin Berkeley. Jack Arnold. Lucas (Nestor Paiva)
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