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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“Help me, Obi Wan Kenobi. You’re my only hope.”
—George Lucas (b. 1944)
“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a sequence of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”
—Philip Roth (b. 1933)