## What is Fibonacci Series?

In Fibonacci series, next number is the sum of previous two numbers. The first two numbers of Fibonacci series are 0 and 1.

The Fibonacci numbers are significantly used in the computational run-time study of algorithm to determine the greatest common divisor of two integers.In arithmetic, the Wythoff array is an infinite matrix of numbers resulting from the Fibonacci sequence.

`The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...`

### Java code using For Loop

```//Using  For Loop
public class FibonacciExample {

public static void main(String[] args)
{
// Set it to the number of elements you want in the Fibonacci Series
int maxNumber = 10;
int previousNumber = 0;
int nextNumber = 1;

System.out.print("Fibonacci Series of "+maxNumber+" numbers:");

for (int i = 1; i <= maxNumber; ++i)
{
System.out.print(previousNumber+" ");
/* On each iteration, we are assigning second number
* to the first number and assigning the sum of last two
* numbers to the second number
*/

int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
}

}

}```
Output:
`Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34`
Program Logic:
• previousNumber is initialized to 0 and nextNumber is initialized to 1
• For Loop iterates through `maxNumber`
• Display the previousNumber
• Calculates sum of previousNumber and nextNumber
• Updates new values of previousNumber and nextNumber

### Java code using While Loop

You can also generate Fibonacci Series using a `While` loop in Java.

```//Using  While Loop
public class FibonacciWhileExample {

public static void main(String[] args)
{

int maxNumber = 10, previousNumber = 0, nextNumber = 1;
System.out.print("Fibonacci Series of "+maxNumber+" numbers:");

int i=1;
while(i <= maxNumber)
{
System.out.print(previousNumber+" ");
int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
i++;
}

}

}```
Output:
`Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34`

The only difference in the program logic is use of WHILE Loop to print Fibonacci Numbers

### Fibonacci Series Based On The User Input

```//fibonacci series based on the user input
import java.util.Scanner;
public class FibonacciExample {

public static void main(String[] args)
{

int maxNumber = 0;
int previousNumber = 0;
int nextNumber = 1;

System.out.println("How many numbers you want in Fibonacci:");
Scanner scanner = new Scanner(System.in);
maxNumber = scanner.nextInt();
System.out.print("Fibonacci Series of "+maxNumber+" numbers:");

for (int i = 1; i <= maxNumber; ++i)
{
System.out.print(previousNumber+" ");
/* On each iteration, we are assigning second number
* to the first number and assigning the sum of last two
* numbers to the second number
*/

int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
}

}

}
```
Program Logic:

The logic is same as earlier. Instead of hardcoding the number of elements to show in Fibonacci Series, the user is asked to write number.

### Java code using Recursion

```//Using Recursion
public class FibonacciCalc{
public static int fibonacciRecursion(int n){
if(n == 0){
return 0;
}
if(n == 1 || n == 2){
return 1;
}
return fibonacciRecursion(n-2) + fibonacciRecursion(n-1);
}
public static void main(String args[]) {
int maxNumber = 10;
System.out.print("Fibonacci Series of "+maxNumber+" numbers: ");
for(int i = 0; i < maxNumber; i++){
System.out.print(fibonacciRecursion(i) +" ");
}
}
}
```
Output:
`Fibonacci Series of 10 numbers: 0 1 1 2 3 5 8 13 21 34`
Program Logic:

A recursive function is one that has the capability to call itself.

fibonacciRecursion():

1. Takes an input number. Checks for 0, 1, 2 and returns 0, 1, 1 accordingly because Fibonacci sequence starts with 0, 1, 1.
2. When input n is >=3, The function will call itself recursively. The call is done two times. Let’s see example for input of 4.
```	fibonacciRecursion (4)
It will recursively call fibonacciRecursion function for values 2 and 3
fibonacciRecursion (2) \\ call for value 0 and 1
fibonacciRecursion (0) = 0
fibonacciRecursion (1) = 1
fibonacciRecursion (3) \\ It will call for 1 and 2
fibonacciRecursion (1) = 1
fibonacciRecursion (2) \\ It will call for 0 and 1
fibonacciRecursion (0) = 0
fibonacciRecursion (1) = 1
```