Search results
Results From The WOW.Com Content Network
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 ...
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.
Generalizations of Fibonacci numbers. In mathematics, the Fibonacci numbers form a sequence defined recursively by: That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1 ...
These indices are all themselves prime. As with the Fibonacci numbers, a Pell number P n can only be prime if n itself is prime, because if d is a divisor of n then P d is a divisor of P n. The only Pell numbers that are squares, cubes, or any higher power of an integer are 0, 1, and 169 = 13 2. [7]
In mathematics and computing, Fibonacci coding is a universal code [citation needed] which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely related to ...
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.
Fibonomial coefficient. In mathematics, the Fibonomial coefficients or Fibonacci-binomial coefficients are defined as. where n and k are non-negative integers, 0 ≤ k ≤ n, Fj is the j -th Fibonacci number and n! F is the n th Fibonorial, i.e. where 0! F, being the empty product, evaluates to 1.
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series. There are various types of generating functions, including ...