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Fibonacci series program in C using recursion

The Fibonacci sequence is a series of numbers where the next number is the addition of the last two numbers, the Fibonacci series starts with 0, and 1.

For example, if we want to find Fibonacci of the 5th term then using recursion we will get the following.

fib(5) = fib(4) + fib(3)

fib(4) = fib(3) + fib(2)

fib(3) = fib(2) + fib(1)

fib(2)=fib(1)+fib(0)

fib(1)=1

fib(0)=0

Fibonacci sequence using recursion diagram

#include<stdio.h>
int fibs(int a)
{ 
  if (a==0) 
    return 0;
  else if(a==1)
    return 1;
  else
    return (fibs(a-1)+fibs(a-2));
}
int main()
{
  int a,i,fib;
  printf("\n enter the fibonacci length:");
  scanf("%d",&a);
  printf("fibonacci series are:");
  for(i=0;i<a;i++)
  {	
    fib=fibs(i);
    printf("%d\t",fib);
  }
  return 0;
}

output

enter the fibonacci length:7
fibonacci series are:0    1       1       2       3       5       8

Explanation of Fibonacci series recursive function program

we declare fibs function i.e Fibonacci series function. it will calculate the Fibonacci series value.
when you run a program, we know our program will always start executing from the main().
so first it will take input from a user and stored it in variable a.

now we call our fibs function from 0 to till a value.

for(i=0;i<a;i++)
  {	
    fib=fibs(i);
    printf("%d\t",fib);
  }

In a for a loop when i value is 0 it will call fibs(0) function, and fibs(0) function will return a value 0. because inside our fibs function we have written
```
 if (a==0) 
   return 0;
```
when i value is 1 it will call fibs(1), the function will return value 1.
```
 else if(a==1)
   return 1;
```
when i value 2, it will call fibs(2). In fibs function, else part gets executed.
```
 else
   return (fibs(a-1)+fibs(a-2));
```
For fibs(2) it call recursively itself for fib(2-1)+ fibs(2-2) i.e fibs(1) and fibs(0).
similarly, it will calculate fibs(3), fibs(4), etc., and print Fibonacci value.

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