Our interpolation conditions are \[ S(1) = S_0(1) = a + b+c +d \] \[ S(2) = S_0(2) = 8a + 4b + 2c + d \] \[ S(2) = S_1(2) = 8e +4f + 2g + h \] \[ S(3) = S_1(3) = 27e + 9f + 9g + h \] \[ S(3) = S_2(3) = 27i + 9j + 9k + l \] \[ S(4) = S_2(4) = 64i + 16j + 4k + l \] \[ S(4) = S_3(4) = 64m + 16n + 4o + p \] \[ S(5) = S_3(5) = 125m + 25n + 5o + p \]