# What is the correct order of DFT values when executing the DIT FFT algorithm?

I was checking the correctness through SageMath (and later through Wolfram Alpha and Mathematica) of some simple whiteboard computations that I've done manually (namely, I have tried to compute the DFT of the simple sequence {0, 1, 2, 3} by using the recursive Decimation-in-time FFT algorithm) and I noticed I'm getting the same values, except 2nd and 4th are switched. What I get is this:  {6, -2 + 2i, -2, -2 - 2i}  while SageMath's result is:  {6, -2 - 2i, -2, -2 + 2i} 

What am I doing wrong here?

Update:

I don't think I am doing anything wrong. Here is the solution without the flow diagram, just using the equations for DIT FFT - I get the same result:

And G and H are following from this:

$$X[k] = \sum_{r=0}^{\frac{N}{2}-1} x[2r]*W_{\frac{N}{2}}^{r*k} + W_N^k*\sum_{r=0}^{\frac{N}{2}-1} x[2r+1]*W_{\frac{N}{2}}^{r*k}$$

$$X[k] = G[k] + W_N^k*H[k]$$ $$X[k + \frac{N}{2}] = G[k] - W_N^k*H[k]$$ where $$k=0,1,...,\frac{N}{2}-1$$

sage: IndexedSequence([0,1,2,3],list(range(4)))