Convert this function from recursive to iterative

Question

def g(n):
"""Return the value of G(n), computed recursively.

>>> g(1)
1
>>> g(2)
2
>>> g(3)
3
>>> g(4)
10
>>> g(5)
22
"""
if n<=3:
    return n
else:
    return g(n-1)+2*g(n-2)+3*g(n-3)

How do I convert this to an iterative function? Until now, I didn't realize that writing a recursive function is sometimes easier than writing an iterative one. The reason why it's so hard I think is because I don't know what operation the function is doing. In the recursive one, it's not obvious what's going on.

I want to write an iterative definition, and I know I need to use a while loop, but each time I try to write one either I add additional parameters to g_iter(n) (when there should only be one), or I make a recursive call. Can someone at least start me off on the right path? You don't have to give me a complete solution.

FYI: We have not learned of the all too common "stack" I'm seeing on all these pages. I would prefer to stay away from this.

def g_iter(n):
"""Return the value of G(n), computed iteratively.

>>> g_iter(1)
1
>>> g_iter(2)
2
>>> g_iter(3)
3
>>> g_iter(4)
10
>>> g_iter(5)
22
"""
"*** YOUR CODE HERE ***"

Answer 1

def g(n):
    if n <= 3:
        return n
    a, b, c = 1, 2, 3
    for i in range(n - 3):
        a, b, c = b, c, c + 2 * b + 3 * a
    return c

---

UPDATE response to comment, without using for loop.

def g(n):
    if n <= 3:
        return n
    a, b, c = 1, 2, 3
    while n > 3:
        a, b, c = b, c, c + 2 * b + 3 * a
        n -= 1
    return c