### David Barksdale

Shared publicly -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]}

#cleaningscrapsofpaperoffmydesk

a[0] = 1

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

#cleaningscrapsofpaperoffmydesk

1