How Fibonacci Series are generated using 1 Variable?

What I am not understanding: How the code is able to generate all the Fibonacci series using just one variable?

#include <stdio.h>
#include <stdlib.h>

int main (void) {
    unsigned long i = 1;
    printf ("0\n");
    while (((i & 0xffff0000) >> 16) + (i & 0xffff) <= 0xffff) {
        printf ("%d\n", i & 0xffff);
        i = ((i & 0xffff) << 16) | ((i >> 16) + (i & 0xffff));
    }
    return 0;
}

Reference: Fabonacci Series using one variable

I don't see why this is hard?
Written in C, demonstrated on IDEOne:

#include <stdio.h>

int fib(int n)
{
    return (n == 0 || n == 1) ?  n : fib(n-1) + fib(n-2);
}

int main(void) {
    int n;
    for(n=0; n<10; ++n)
        printf("[%d] : %d\n", n, fib(n));

    return 0;
}

I only see 1 variable.
Does that not meet your requirement?

Output

[0] : 0
[1] : 1
[2] : 1
[3] : 2
[4] : 3
[5] : 5
[6] : 8
[7] : 13
[8] : 21
[9] : 34

If you want to be tricky, use the wonderful expression n==!!n?n:

int fib(int n)
{
    return n==!!n?n: fib(n-1) + fib(n-2);
}