OFFSET
1,2
COMMENTS
A nonempty word w is a border of a string x if w is both a prefix and suffix of x, and w does not equal x.
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)
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 15 2020
EXTENSIONS
More terms from Rémy Sigrist, Jan 15 2020
STATUS
approved