Improve this recursive code please!

[Steven Taschuk]

Quoth andrew cooke:
  [...]
> search for 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490
> at http://www.research.att.com/~njas/sequences/
> (or sequence number A000041)
> 
> it returns a single result - i can't work out how to link directly - and
> there's no nice simple formula (which cheered me up because i spent a
> while trying to figure one out, but couldn't).

Ah, but that's the partition function p(n), the number of ways to
store n bricks in any number of bins, where each bin is nonempty,
and bins are not considered distinct.  For example,
    4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1
showing that p(4) = 5.  This is the answer to a different problem;
in the OP's code, the bins are considered distinct, and there's a
maximum number of bins.  That turns out to be more tractable; see
my other post of a few minutes ago for a closed-ish form.

(A direct link for the above sequence:
    <http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000041>
.)

-- 
Steven Taschuk                               staschuk at telusplanet.net
"What I find most baffling about that song is that it was not a hit."
                                          -- Tony Dylan Davis (CKUA)