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A structure similar to LCGs, but not equivalent, is the multiple-recursive generator: X n = (a 1 X n−1 + a 2 X n−2 + ··· + a k X n−k) mod m for k ≥ 2. With a prime modulus, this can generate periods up to m k −1, so is a useful extension of the LCG structure to larger periods.
In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation.Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
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.
Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion ...
In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
is constant-recursive because it satisfies the linear recurrence = +: each number in the sequence is the sum of the previous two. [2] Other examples include the power of two sequence 1 , 2 , 4 , 8 , 16 , … {\displaystyle 1,2,4,8,16,\ldots } , where each number is the sum of twice the previous number, and the square number sequence 0 , 1 , 4 ...
The most important basic example of a datatype that can be defined by mutual recursion is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children). This ...
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest [1] and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are ...