

A331392


Sum, over all binary strings w of length n, of the length of the shortest border of w.


1



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
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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.


LINKS

Table of n, a(n) for n=1..33.


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*k1) + 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

Cf. A045690, A091065, A331393.
Sequence in context: A233411 A057422 A036045 * A100538 A303794 A135139
Adjacent sequences: A331389 A331390 A331391 * A331393 A331394 A331395


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Jan 15 2020


EXTENSIONS

More terms from Rémy Sigrist, Jan 15 2020


STATUS

approved



