Question

Find the equation which yields the Nth term of the sequence: 0,1,1,3,5,17,28,105,161,670,1001,2869. . .

Answer 1

Where did you find this problem?

Note that, like all sequences defined this way, there are an infinite number of possibilities that you can have for what this sequence is. However one thing that comes to mind is this: place n points on a circle so that they are equally spaced. Let A be the set of all paths connecting the n points (not closed). Then this sequence is the number of different lengths of elements of A.

Answer 2

Yes, that is close to what it represents. I published this in the encycylopedia of integer sequences. All due respect for finding just what my sequence represents, the question is find an equation for the next term/ Precisely, the sequence represents the number of Unique Path Lengths that exist for the permutative exhaustive association by linear line segments joining n number of points equidistantly positioned on the unit circle. I know, I'm the author of the sequence. Can you suggest the Nth term equation ? One more hint, there is only ONE sequential solution given the parameters of the sequence. A certain number of points will yield only one value that represents the total number of Unique Path Lengths given the geometric constraint of circular boundry and equidistant positioning of the points along the circle. I am impressed by your profile, so in keeping the spirit alive allow me to ask; you did state a year of study in the diifferential geometry- If we were to extend the equidistant positioning to three dimentions, a sphere, do the values for the number of Unique Path Lengths remain invariant ?

Answer 3

One more hint, the mathematician that extended my sequence past 2869- although not in words, suggests that the sequence diverges chaotically from what appears to be a uniform progression of an increase in the UPL (Unique Path Lengths)-can you theorize what the significance of this may be ?