I am really sad and I noticed that the sequence:
$0 , 1 , 2$
Has its sum equal to its length.
I was wondering how many these existed.
e.g:
$ 1$
$-3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5$ $(= 9)$
I got so far and got stuck, I reduced it down to finding out how many solutions there are to the equation:
$m^2 - n^2 + m + n = 0$ , $0 < n < m$
Can anyone tell me how to find this out?