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The Fibonacci sequence is a sequence of numbers in which each successive number in the sequence is obtained by adding the two previous numbers in the sequence. The sequence is named after the Italian mathematician Fibonacci. The sequence starts with zero and one, and proceeds forth as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. The Fibonacci sequence is widely used in applications pertaining to mathematics, science, computers, art and nature.
The Fibonacci sequence is also known as the Fibonacci series or Fibonacci numbers.
The Fibonacci sequence is a simple, yet complete sequence, i.e all positive integers in the sequence can be computed as a sum of Fibonacci numbers with any integer being used once at most. Similar to all sequences, the Fibonacci sequence can also be evaluated with the help of a finite number of operations. In other words, the Fibonacci sequence has a closed-form solution. The general rule to obtain the nth number in the sequence is by adding previous (n-1)th term and (n-2) term, i.e. xn = xn-1 + xn-2.
The Fibonacci sequence has been used in many applications. Computer algorithms such as Fibonacci search techniques and Fibonacci heap data structure make use of the Fibonacci sequence, as do recursive programming algorithms. Another use of the Fibonacci sequence is in graphs called Fibonacci cubes, which are made to interconnect distributed and parallel systems. Some pseudorandom number generators also make use of Fibonnaci numbers. Nature makes use of the Fibonacci sequence as well, for example, in the case of branching in trees.