A331393 Sum, over all binary strings w of length n, of the length of the longest border of w.

0, 2, 6, 16, 36, 82, 176, 372, 768, 1582, 3224, 6534, 13166, 26504, 53244, 106824, 214060, 428764, 858400, 1718056, 3437734, 6877896, 13759154, 27523128, 55052582, 110114618, 220242288, 440503282, 881031714, 1762100362, 3524251618, 7048576724, 14097253490

Offset: 1

Author

Jeffrey Shallit, Jan 15 2020

Keywords

• nonn

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.

Examples

			For n = 4 the 16 words are 0000,0001,0010,0011,0100,0101,0110,0111, and their binary complements.
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.
		

Links

• Shiyao Guo, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A094536, A331392.

Extensions

More terms from Rémy Sigrist, Jan 16 2020