n should be the correct answer.
T(n) = T(n - 1) + T(n - 2) - T(n - 3)
T(n - 1) = T(n - 2) + T(n - 3) - T(n - 4)
T(n - 2) = T (n - 3) + T(n - 4) - T(n - 5)
T(n - 3) = T (n - 4) + T(n - 5) - T(n - 6)
T(n - 4) = T (n - 5) + T(n - 6) - T(n - 7)
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T(6) = T(5) + T(4) - T(3)
T(5) = T(4) + T(3) - T(2)
T(4) = T(3) + T(2) - T(1)
On Adding all the above recurrences, all the red terms of a recurrence will be cancelled out with the red terms of consecutive recurrences, similarly all the blue terms of a recurrence will be cancelled out with the blue terms of consecutive recurrences.
Thus we get
T(n) = T(n - 2) + T(3) - T(1),
but since T(3) =3 & T(1) = 1
so our final recurrence will be T(n) = T(n - 2) + 2
Solution of T(n) = T(n - 2) + 2 will be n.