Q:

How to sample only odd numbers in the domain of a table for list plot

The following code samples $k$ points around a circle at integer values starting from $0$:
ListPlot[Table[{2 Sin[(2*y/x)*π*n] , 2 Cos[(2*y/x)*π*n}], {n, 0, k}]

I wish instead to sample every other point. So instead of running $n$ from $0$ to $k$, I want the function plotted at $n=0,2,4,...2m$ or $n=1,3,5,...2r+1$ (I am assuming that the method is the same for both of these cases). How can I implement this? 

A:

First I will rework your code to show where the points lie on the plot.
With[{x = 11, y = 3, k = 7},
  ListPlot[
    Table[{{2 Sin[(2*y/x)*π*n], 2 Cos[(2*y/x)*π*n]}}, {n, 0, k}],
    PlotStyle -> {{Red, FontSize -> 20}},
    PlotMarkers -> {0, 1, 2, 3, 4, 5, 6, 7}]]

Now I will pick only the odd numbered points
With[{x = 11, y = 3, k = 7},
  ListPlot[
    Table[{{2 Sin[(2*y/x)*π*n], 2 Cos[(2*y/x)*π*n]}}, {n, 1, k, 2}],
    PlotStyle -> {{Red, FontSize -> 20}},
    PlotMarkers -> {1, 3, 5, 7}]]

and here I pick the even numbered points
With[{x = 11, y = 3, k = 7},
   ListPlot[
     Table[{{2 Sin[(2*y/x)*π*n], 2 Cos[(2*y/x)*π*n]}}, {n, 0, k, 2}],
     PlotStyle -> {{Red, FontSize -> 20}},
     PlotMarkers -> {0, 2, 4, 6}]]]

