A331392 Sum, over all binary strings w of length n, of the length of the shortest border of w.
0, 2, 4, 12, 24, 60, 120, 264, 528, 1116, 2232, 4584, 9168, 18616, 37232, 75056, 150112, 301556, 603112, 1209064, 2418128, 4842504, 9685008, 19383408, 38766816, 77562648, 155125296, 310312528, 620625056, 1241382832, 2482765664, 4965813280, 9931626560
Offset: 1
Keywords
Examples
For n = 3, the words are 000,001,010,011 and their binary complements. The shortest border of 000 and 010 is 0, and the other words have no border. So a(3) = 4.
Formula
From Rémy Sigrist, Jan 16 2020: (Start)
Apparently, for any k > 0:
- a(2*k+1) = 2*a(k),
- a(2*k) = 2*a(2*k-1) + 2*k*A045690(k).
(End)
Extensions
More terms from Rémy Sigrist, Jan 15 2020
Comments