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A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as t, one period earlier denoted as t − 1, one period later as t + 1, etc. The solution of such an equation is a function of t, and not of any
A famous example is the recurrence for the Fibonacci numbers, = + where the order is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients , because the coefficients of the linear function (1 and 1) are constants that do not depend on n . {\displaystyle n.}
The equation is called a linear recurrence with constant coefficients of order d. The order of the sequence is the smallest positive integer such that the sequence satisfies a recurrence of order d, or = for the everywhere-zero sequence. [citation needed]
In mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials.P-recursive equations are linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomial coefficients.
In mathematics, and especially in numerical analysis, a homogeneous linear three-term recurrence relation (TTRR, the qualifiers "homogeneous linear" are usually taken for granted) [1] is a recurrence relation of the form
Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. [2] George Pólya writes in Mathematics and plausible reasoning: The name "generating function" is due to Laplace. Yet, without giving it a name, Euler used the
Adding a non-linear output mixing function (as in the xoshiro256** and permuted congruential generator constructions) can greatly improve the performance on statistical tests. Another structure for a PRNG is a very simple recurrence function combined with a powerful output mixing function.
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 (,).
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