In Fibonacci Series, next number use the sum of the previous two numbers. For example: 0, 1, 1, 2, 3, 5 , 8, 13, 21, 34, 55 and so on. Fibonacci series starts from 0 and 1.

Fibonacci application are in Stock Market, Trading, Banking Application, Data structure, Graphs and much more.

The sequence Fn of Fibonacci numbers is defined by the recurrence relation:
Fn = Fn-1 + Fn-2
There are two ways to write the Fibonacci Series program in java:
  • Fibonacci Series without using recursion
  • Fibonacci Series using recursion

Fibonacci Series in Java using without Recursion

class FibonacciExample1{
public static void main(String args[])
{  
 int n1=0,n2=1,n3,i,count=10;  
 System.out.print(n1+" "+n2);//printing 0 and 1  
  
 for(i=2;i < count;++i)//loop starts from 2 because 0 and 1 are already printed  
 {  
  n3=n1+n2;  
  System.out.print(" "+n3);  
  n1=n2;  
  n2=n3;  
 }  


Fibonacci Series in Java using with Recursion

class FibonacciExample2{
 static int n1=0,n2=1,n3=0;  
 static void printFibonacci(int count){  
    if(count > 0){  
         n3 = n1 + n2;  
         n1 = n2;  
         n2 = n3;  
         System.out.print(" "+n3); 
         printFibonacci(count-1);  
     }  
 }  
 public static void main(String args[]){  
  int count=10;  
  System.out.print(n1+" "+n2);//printing 0 and 1  
  printFibonacci(count-2);//n-2 because 2 numbers are already printed 
 }
}

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Fibonacci Series Examples:

A tiling with squares whose side lengths are successive Fibonacci numbers
A tiling with squares whose side lengths are successive Fibonacci numbers
Source Wikipedia