The sum of all natural numbers smaller than and including x is equal to

(X+1)(x/2)

The sum of all even numbers up to and including x is that minus (n/2)² so

[(X+1)(x/2)]-(x/2)²

That would mean the sum of all odd numbers under x is equal to

(x/2)²

or sum of all odd including x (if x is odd of course) is

[(x+1)/2]²

Since the sum of all even numbers up to x is the sum of all numbers minus the sum of all odd numbers.

[-(X/2)² +2x +1]/2 (another way of writing the sum of all evens under and including a number) looks suspiciously polynomial. I want to go further.