Search results
Results From The WOW.Com Content Network
The Fibonacci sequence is constant-recursive: each element of the sequence is the sum of the previous two. Hasse diagram of some subclasses of constant-recursive sequences, ordered by inclusion In mathematics , an infinite sequence of numbers s 0 , s 1 , s 2 , s 3 , … {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant ...
In mathematics, the Skolem problem is the problem of determining whether the values of a constant-recursive sequence include the number zero. The problem can be formulated for recurrences over different types of numbers, including integers, rational numbers, and algebraic numbers.
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
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.
Let () be a sequence of complex numbers satisfying () = + + + for all , where are complex number constants (i.e., a constant-recursive sequence of order ).Then the set of zeros {() =} is equal to the union of a finite set and finitely many arithmetic progressions.
The sequence of permutations generated by the Steinhaus–Johnson–Trotter algorithm has a natural recursive structure, that can be generated by a recursive algorithm. However the actual Steinhaus–Johnson–Trotter algorithm does not use recursion, instead computing the same sequence of permutations by a simple iterative method.
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 (,).
In mathematics, the Hofstadter Female and Male sequences are an example of a pair of integer sequences defined in a mutually recursive manner. Fractals can be computed (up to a given resolution) by recursive functions. This can sometimes be done more elegantly via mutually recursive functions; the Sierpiński curve is a good example.