#ES6 (Javascript), <del>79</del>, 70 bytes#

Can certainly be golfed further.

**Golfed**

    S=(n,a,i=0)=>i<n-2?a.push(eval(a[i]+"+*-/"[i%4]+a[i+1]))&&S(n,a,i+1):a

**Test**

    S=(n,a,i=0)=>{a.push(eval(a[i]+"+*-/"[i%4]+a[i+1]));(i<n-3)&&S(n,a,i+1);return a}

    >S(5,[0,1])
    Array [ 0, 1, 1, 1, 0 ]