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%I #14 Feb 25 2021 02:18:59
%S 0,2,6,16,36,82,176,372,768,1582,3224,6534,13166,26504,53244,106824,
%T 214060,428764,858400,1718056,3437734,6877896,13759154,27523128,
%U 55052582,110114618,220242288,440503282,881031714,1762100362,3524251618,7048576724,14097253490
%N Sum, over all binary strings w of length n, of the length of the longest border of w.
%C 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.
%H Shiyao Guo, <a href="/A331393/b331393.txt">Table of n, a(n) for n = 1..120</a>
%e For n = 4 the 16 words are 0000,0001,0010,0011,0100,0101,0110,0111, and their binary complements.
%e 0000 has longest border 3; 0010, 0100, 0110 have longest border 1; and 0101 has longest border 2. So a(4) = 2*(3+3+2) = 16.
%Y Cf. A094536, A331392.
%K nonn
%O 1,2
%A _Jeffrey Shallit_, Jan 15 2020
%E More terms from _Rémy Sigrist_, Jan 16 2020
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