Place 
balls in a bag and number them 1 to 
, then pick half of them at random. The number of different
possible sums for 
,
2, 3, ... are then 2, 5, 10, 17, 26, ... (OEIS A002522),
or 
Number Picking
See also
Number Guessing, Real Number PickingExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A002522 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Number PickingCite this as:
Weisstein, Eric W. "Number Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NumberPicking.html