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

1,2

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

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

Example

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.

Crossrefs

Cf. A094536, A331392.

Sequence in context: A066641 A265106 A306332 * A026540 A351932 A329256

Adjacent sequences: A331390 A331391 A331392 * A331394 A331395 A331396

Keyword

nonn

Author

Jeffrey Shallit, Jan 15 2020

Extensions

More terms from Rémy Sigrist, Jan 16 2020

Status

approved