Typical "stars" are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA, with the order of the points going clockwise being A, B, C, D, and E.

The segments must always skip a constant number of points which is at least one.

Given the information that there is only 1 way to draw a 5-point star, and that there is NO way to draw a 6-point star (in continuous lines, that is), and there are 2 ways to draw a 7-point star.

How many different ways are there to draw a 1000-point star?