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

    >S(8,[1,3]
    Array [ 1, 3, 4, 12, -8, -1.5, -9.5, 14.25 ]

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

    >S(9,[1,0])
    Array [ 1, 0, 1, 0, 1, 0, 1, 0, 1 ]

    >S(25,[6,3])
    Array [ 6, 3, 9, 27, -18, -1.5, -19.5, 29.25, -48.75, -0.6, ...]