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
Famous quotes containing the words lucas and/or sequence:
“When posterity judges our actions here it will perhaps see us not as unwilling prisoners but as men who for whatever reason preferred to remain non-contributing individuals on the edge of society.”
—George Lucas (b. 1944)
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)