A025591 and subset sums

[Eric W. Weisstein]

On Thu, 11 Dec 2003, Edwin Clark wrote:

> On Fri, 12 Dec 2003, Yuval Dekel wrote:
> 
> > If my memory is not mistaken, sequence A025591 is related to the following
> > paper :
> >
> > Robert A. Proctor
> > Solution of two difficult combinatorial problems with linear algebra,
> > American Mathematical Monthly 89, 721-734.
> 
> Here's the abstract. I don't see the connection.

A025591(n) is the maximal number of subsets of $\{1,2,\dots,n\}$ that
share the same sum:

<<DiscreteMath`Combinatorica`
Max/@Map[Length,Split/@Sort/@((Plus@@@Subsets[#])&/@Range[10]),{2}]
{1,1,2,2,3,5,8,14,23,40}

Cheers,
-E