summation result

Question

I have an array A = [1,2,3] I need to find the array B[i] with the below statement. calculation i did:
B[0] = A[1] + F[0]
        1 + F[0] = 1+0=2 hence B=[1]
        1 + F[1] = 1+2=3 hence B=[1,2]
        1 + F[2] = 1+3=4 hence B=[1,3,4] but the ans is [1,3,5] how?
       0
F[0] = Σ A[2 * (0/2)] = A[0]=0 since array A is 1 based index
       j=2

       1
F[1] = Σ A[2 * (1/2)] = A[1]= 2
       j=2

       2
F[2] = Σ A[2 * (2/2)] = A[2]= 2
       j=2


B[i] = A[1] + F[i]

F[i] = 0,1 <= i < k

       i
F[i] = Σ A[k * (j/k)]
       j=k

where A=[1,2,3] // 1 based index
k=2
what is the value of B