Search results
Results From The WOW.Com Content Network
A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a recurrence relation has the form. where. is a function, where X is a set to which the elements of a sequence must belong.
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...
The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively. A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying ...
A linear recurrence with constant coefficients is an equation of the following form, written in terms of parameters a1, ..., an and b: or equivalently as. The positive integer is called the order of the recurrence and denotes the longest time lag between iterates. The equation is called homogeneous if b = 0 and nonhomogeneous if b ≠ 0.
In mathematics, an infinite sequence of numbers is called constant-recursive if it satisfies an equation of the form. for all , where are constants. The equation is called a linear recurrence relation. The concept is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, or a C-finite sequence.
φ(n) is the number of positive integers not greater than n that are coprime with n. A000010. Lucas numbers L(n) 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032. Prime numbers pn. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers pn, with n ≥ 1.
A Pythagorean triple can be generated using any two positive integers by the following procedures using generalized Fibonacci sequences. For initial positive integers hn and hn+1, if hn + hn+1 = hn+2 and hn+1 + hn+2 = hn+3, then. is a Pythagorean triple.
v. t. e. In mathematics, an arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. The n th term of an arithmetico-geometric sequence is the product of the n th term of an arithmetic sequence and the n th term of a geometric sequence. [1]