number of different outcomes

[Robert G. Wilson v]

"Eric W. Weisstein" wrote:

> On Mon, 11 Oct 1999, vdmcc wrote:
>
> > Put 2n balls in a bag, numbered 1 to 2n. Pull out half of them at
> > random and add their values. How many different sums are possible?
> >
> > n      outcomes
> > 0    1
> > 1    1
> > 2    2
> > 3    3
> > 4    6
> > 5    12
> > 6    17
> > 7    24
> > 8    32
> > 9    40
>
> What am I missing?  (Surely a(1)=2 in the above problem?)
>
> Table[Length[Union[Plus @@@ KSubsets[Range[2n], n]]], {n, 7}]
> {2, 5, 10, 17, 26, 37, 50}
>
> Cheers,
> -Eric

I'm with you.  Notice that the first difference of your calculation are
the odd numbers.

Bob.