The time complexity of a non-standard recursive fibonacci series

#1

So I was attempting to create a recursive fibonacci series algorithm on my own, similar to this example, just for fun. Then I discovered that its temporal complexity is of the order O(n). However, according to my study, the recursive fibonacci series method has a temporal complexity of O(2n)??

This is my C code:

#include <stdio.h>
void fibonacci(int n){
    int static a,b,c; //SO THAT VARIABLES CAN BE SHARED ACROSS FUNCTION CALLS
    if (n > 2)
    {
        fibonacci(n-1);
        c = a + b;
        printf("%d ",c);
        a = b;
        b = c;
    }
    if (n < 3)
    {
        a = 0;
        b = 1;
        if (n < 2)
        {
            printf("%d ",a);
        }
        else
        {
            printf("%d %d ",a,b);
        }   
    }
}

int main()
{
    fibonacci(10); //FINDING THE FIRST 10 FIBONACCI NUMBERS
    return 0;
}

I understand that the use of static variables has altered something, but I’m not sure what and would appreciate a more detailed explanation!

I’ve been having difficulties calculating temporal complexity of recursive algorithms in general, so please forgive me if this is a minor issue. Thanks