number of different outcomes

[Eric W. Weisstein]

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

--------------------------------------------------------------------
* Eric W. Weisstein                                                *
* Encyclopedist             phone:  217-398-0700 x599              *
* Wolfram Research, Inc.    FAX:    217-398-0747                   *
* 100 Trade Center Drive    e-mail: eww at wolfram.com                *
* Champaign, IL 61820-7237  WWW: www.treasure-troves.com/eric.html *
--------------------------------------------------------------------