Flatten[{1,0,0}/.{1{0,0},0{0,1}}]
{0,0,0,1,0,1}
Nest[Flatten[#/.{1{0,0},0{0,1}}]&,{1},10]
Fourier
ListPlot[Abs[Fourier[%5]]^2,PlotRangeAll,PlotJoinedTrue]
⁃Graphics⁃
ListPlot[Abs[Fourier[%5,FourierParameters{1,-1}]]^2,PlotRangeAll,PlotJoinedTrue]
dft[u_]:=With[{n=Length[u]},Sum[u[[r]]Exp[2PiI(r-1)(s-1)/n]/Sqrt[n],{r,1,n}]]
dft[Array[a,4]]
a[1]
2
1
2
1
2
1
2
π(-1+s)
1
2
3
2