Puzzle: Writting year as sums of runs of numbers

This year is 2016 and \[ 2016 = 1 + 2 + 3 + ... + 63 \] I didn't notice this myself, I saw it written somewhere but then I wondered if there were any other ways of writing 2016 as a sum of consecutive numbers and it turn out there are.

So, the puzzle is, how many ways are there of writing 2016 as a sum of consecutive numbers and what's the answer for the general case where you're trying to write any number \(Y\) as such a sum. The answer is quite simple but non-obvious.

I'll post the solution shortly My solution is here, please leave comments or solutions below.