# Mathematica, <s>49</s> 48 bytes

    ±2=4;±1=0;±n_:=Tr@Range@±(n-1)-Tr@Array[±#&,n-1]
    (* or *)
    ±2=4;±1=0;±n_:=-Tr@Array[(k=±#)&,n-1]+Tr@Range@k

Uses CP-1252 encoding. Defines function `PlusMinus (±)`. 1-indexed.

# Explanation

    ±2=4;±1=0;±n_:=Tr@Range@±(n-1)-Tr@Array[±#&,n-1]
    
    ±2=4;±1=0;                                        (* Define ±1 and ±2 *)
              ±n_:=                                   (* ±n equals ... *)
                   Tr@Range@±(n-1)                    (* Sum of (1, 2, ..., ±(n-1)) ... *)
                                  -Tr@Array[±#&,n-1]  (* Minus the sum of previous terms *)