/sci/ - Science & Math

Where does this 2 come from?

It works, but i dont understand why.

a[n] = a[n-1] - n, where a[0] = 4

i got a[n] = (((a[n-3] - (n-2)) - (n-1)) - n)
= a[n-3] - 3n +3
= a[n-3] - 3(n+1)
= a[n-n] - n(n+1)
= a[0] - n(n+1)
= 4 - n(n+1)

but it should be a[n] = 4 - n(n+1)/2