[plt-scheme] DrScheme crash, and my bad programming

I know that there's probably a more conventional way to write code
like this -- this is just my dorky translation of a C for loop into a
recursion.

(define (solution6? a b c d n)
  (let ([f (- (* 12 n (- n 2)) b (* 3 c) (* 2 d))])
    (and (>= f 0)
         (>= (* n n n) (+ a b c d (- (* 8 n) (* 2 a) b) f)))))

(define (count-solutions a b c d n)
  (cond
    [(> a (* 4 n)) 0]
    [(> b (- (* 8 n) (* 2 a))) (count-solutions (add1 a) 0 0 0 n)]
    [(> c (- (* 4 n (- n 2)) b)) (count-solutions a (add1 b) 0 0 n)]
    [(> d (quotient (- (* 12 n (- n 2))
                       b
                       (* 3 c))
                    2)) (count-solutions a b (add1 c) 0 n)]
    [(solution6? a b c d n) (add1 (count-solutions a b c (add1 d) n))]
    [else (count-solutions a b c (add1 d) n)]))

But if you run (count-solutions 0 0 0 0 10) or so,
where the recursion is then going a couple hundred million layers deep,
DrScheme crashes.

If I break up the recursion into one function that recurses on c and d
while another recurses on a and b, then it has no trouble.

If you want me to be more specific about exactly what code I run to
make DrScheme crash, let me know.  (By crash, I mean the application
quits -- v372 on OS X 10.4)

But I'm also writing because I figure there are more elegant ways to
write for-loop-esque code like this -- maybe I should post that to
plt-edu instead -- but I'd love to learn what the conventional way is
to write this type of code.  Something with let loop?  I've seen that
idiom but I don't really get it.

Finally, the algorithm here is just brute-force counting of solutions
to a system of three linear diophantine equations in seven variables,
where all the variables have to be nonnegative.  So I pick 4 of them,
look at all the possibilities, and check for whether the remaining
values are positive (with a few shortcuts, since the limits of the
loop guarantee some of them will be positive).  So maybe there are
much much much more efficient ways of counting the number of solutions
to a system like this?  (Equivalently, the number of lattice points in
a 7-dimensional region bounded by a bunch of hyperplanes.)

Thanks!
--Joshua Zucker