I have a sequence $(u_{n})$ $$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$ I want to list the first 20$20$ terms of this sequence and find the sum of all terms and sum of all even numbers of 20$20$ terms. I tried
Clear[u];
u[1] := 1; u[2] := 2;
u[3] := 3;
u[y_] := -u[y - 3] + 3u[y - 2] + 2u[y - 1]
A := Table[ u[k], {k, 1, 20}]
Sum[ A[[i]], {i, 1, Length[A]}]
I can't find sum of even numbers. How do I tell Mathematica to do that ?