Not to be confused with the sequence of Lucas numbers, which is a particular Lucas sequence.
In mathematics, the Lucas sequences and are certain constant-recursive integer sequences that satisfy the recurrence relation
where and are fixed integers. Any sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences and
More generally, Lucas sequences and represent sequences of polynomials in and 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 (see below). Lucas sequences are named after the French mathematician Édouard Lucas.
superset of Fermat numbers (see below). Lucassequences are named after the French mathematician Édouard Lucas. Given two integer parameters P {\displaystyle...
The Lucassequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and...
numbers pass: in this case, criteria relative to some Lucassequence. Baillie and Wagstaff define Lucas pseudoprimes as follows: Given integers P and Q, where...
derived from it to John Pell. The Pell–Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this type; the...
related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucassequences. The Fibonacci...
the Lucassequence is the second row. See also Fibonacci integer sequences modulo n. A different generalization of the Fibonacci sequence is the Lucas sequences...
integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucassequence U n...
polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers...
In mathematics, a Lehmer sequence is a generalization of a Lucassequence. If a and b are complex numbers with a + b = R {\displaystyle a+b={\sqrt {R}}}...
preceding denominator to form the new numerator. This sequence of denominators is a particular Lucassequence known as the Pell numbers. We can gain further...
as assistant editors, including George Lucas. The following spring, the newly engaged Marcia moved in with Lucas at his hilltop apartment on Portola Drive...
The sequence of Lucas numbers (not to be confused with the generalized Lucassequences, of which this is part) is like the Fibonacci sequence, in which...
mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Édouard Lucas. It is a sequence a0, a1, a2, a3,...
Lucas has founded and supported multiple philanthropic organizations and campaigns dedicated to education and the arts, including the George Lucas Educational...
integer sequence with characteristic equation x3 = x + 1. The Perrin numbers bear the same relationship to the Padovan sequence as the Lucas numbers do...
following, particularly in the aftermath of Lucas's success with Star Wars (1977). A director's cut prepared by Lucas was released in 2004. In the dystopian...
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula...
divisibility sequence. More generally, any Lucassequence of the first kind Un(P,Q) is a divisibility sequence. Moreover, it is a strong divisibility sequence when...
Loyola University Chicago Land-use change LUC, cryptosystem based on Lucassequences Château de Luc, a French castle-ruin in the town of Luc in the Lozère...
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