Mathematica does not like this recurrence relation. I do not understand why?
RSolve[{a[0] == 1,
a[n] == 2 + 2 a[0] + 2 Sum[a[i], {i, 1, n - 2}] + a[n - 1],
a[1] == 3, a[2] == 7}, a, n]
Table[a[n] /. First[%], {n, 10}]
If I change the 1 in the sum to n-3 or something, that it seems to be okay. But why can't I sum from 1 to n-2?