Question

What is the sequence of the diagonals of a polygon?

Answer 1

`{ (a_1 = 0), (a_2 = 0), (a_n = (n(n-3))/2" for "n >= 3) :}`

Explanation:

I think you are wanting to know what the number of diagonals of a convex `n` sided polygon for any `n`, with the resulting sequence.

A diagonal runs from one vertex to a distinct non-adjacent vertex, of which there are `n-3` possibilities.

Hence the formula for the number of diagonals of an `n`-sided convex polynomial is:

`(n(n-3))/2`

which is valid for any `n >= 3`

So we can define a corresponding sequence by:

`{ (a_1 = 0), (a_2 = 0), (a_n = (n(n-3))/2" for "n >= 3) :}`

The first few terms are:

`0, 0, 0, 2, 5, 9, 14, 20,...`