Quote:
Originally Posted by mfgoode
The 1st 5 terms are in G.P but from the 6th T6 =31 and not 32 as expected.

But that expectation of 32 is based on an assumption that powers of 2 are involved, just because the first few terms of the sequence are equal to powers of 2.
That assumption would probably not survive a thoughtful comparison of diagrams with
n points and the connecting diagonals, for
n= 2, 3, 4, 5, ... One would soon note, for example, that
each time a point is added, one more region bordering the circle is created.
There are [b]n[/b] such regions between the circle and the inscribed [b]n[/b]sided polygon.
When one subtracts [b]n[/b] from T[b]n[/b], one is left with the number of regions inside the polygon.
But soon that doesn't jibe with a 2^([b]n[/b]1) assumption ...
This would lead to one of your three ways of representing T
n, I suppose.

P.S. Why does the spoiler tag interfere with wordwrapping when I don't explicitly include line breaks? Or is that just on my browser?