A person would just write down the values as
they were computed and add up the last two to get the next one; no
sequence value would ever be computed twice.
To imitate the pencil-and-paper process, you
would write a loop to compute Fibonacci numbers.
int fib(int n)
{
if (n <= 2) return 1;
int fold = 1;
int fold2 = 1;
int fnew;
for (int i = 3; i <= n; i++)
{
fnew = fold + fold2;
fold2 = fold;
fold = fnew;
}
return fnew;
}