100,000 stars

Check out this site aswell.

http://www.atlasoftheuniverse.com/index.html

It's quite astonishing really how fast the amount of stars increases by just increasing the radius of your sphere of influence a little bit. All thanks to this little formula (4/3 * pi * R^3) for volume of a sphere

There's around 100 stars within 20ly of earth, and already 2000 within 50ly. extrapolating that would get you 16000 within 100ly and 128000 within 200ly.
This will be about the volume occupied by the human colonized systems in Elite.

Just adding 25% to your radius is enough to double the amount of stars within reach.
 
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