No. I am asking about the areas partitioned, not the number of lines.

Let me rephrase the question. Let's say you have 3 randomly points placed interior or inside a circle . The three non collinear points will determine 3 chords inside the circle if I draw lines connecting every two points. A chord is a line drawn inside a circle which stops at the circumference. Now two points determine a chord. So 3 points will make 3 chords. I am not asking about the number of lines, I am asking about the areas partitioned. For 3 points I get 7 areas are partitioned. Please try this. Draw a circle, place 3 points. Try chords connecting the dots. So you should get get 7 areas for 3 chords. The sequence starts with 1 because 1 point has 1 area partitioned, 2 points make 1 chord which gives you 2 areas partitioned, etc so
How many areas are partioned in the circle given n points (any 3 non collinear) and chords drawn through any 2 points.
The sequence is
1,2,7,16,31,54...