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  2. Recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Recurrence_relation

    In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.

  3. Linear recurrence with constant coefficients - Wikipedia

    en.wikipedia.org/wiki/Linear_recurrence_with...

    In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.

  4. Three-term recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Three-term_recurrence_relation

    If the {} and {} are constant and independent of the step index n, then the TTRR is a Linear recurrence with constant coefficients of order 2. Arguably the simplest, and most prominent, example for this case is the Fibonacci sequence , which has constant coefficients a n = b n = 1 {\displaystyle a_{n}=b_{n}=1} .

  5. Constant-recursive sequence - Wikipedia

    en.wikipedia.org/wiki/Constant-recursive_sequence

    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]

  6. P-recursive equation - Wikipedia

    en.wikipedia.org/wiki/P-recursive_equation

    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.

  7. Skolem problem - Wikipedia

    en.wikipedia.org/wiki/Skolem_problem

    A linear recurrence relation expresses the values of a sequence of numbers as a linear combination of earlier values; for instance, the Fibonacci numbers may be defined from the recurrence relation F(n) = F(n − 1) + F(n − 2) together with the initial values F(0) = 0 and F(1) = 1.

  8. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    This is a second order nonlinear recurrence with constant coefficients. When the common ratio of a geometric sequence is positive, the sequence's terms will all share the sign of the first term. When the common ratio of a geometric sequence is negative, the sequence's terms alternate between positive and negative; this is called an alternating ...

  9. Lehmer sequence - Wikipedia

    en.wikipedia.org/wiki/Lehmer_sequence

    2 Recurrence. 3 References. ... Lehmer numbers form a linear recurrence relation with = ... Statistics; Cookie statement; Mobile view ...