**If you have a unit interval and you want to know how many ways you can divide it such that division marks...**

If you have a unit interval and you want to know how many ways you can divide it such that division marks are at m/2^n and the divisions are sorted from smallest to largest, use this recurrence relation:

a[0] = 1

a[n] = 1 + sum_{i=0}^{n-1} {2^(i(n-i-1))a[i]}

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Syndicated 2012-12-06 03:01:38 from David Barksdale - Google+ Posts