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A295499 Sum of lengths of longest unbordered subword, over all binary words of length n. 0
2, 6, 18, 48, 124, 302, 720, 1672, 3828, 8624, 19222, 42402, 92824, 201730, 435848, 936548, 2003292, 4267162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By "subword" we mean a contiguous substring within a word.  A string x is "bordered" if it has some nonempty prefix (other than x) that is also a suffix, and "unbordered" otherwise.

REFERENCES

Pawel Gawrychowski, Gregory Kucherov, Benjamin Sach, and Tatiana Starikovskaya, "Computing the Longest Unbordered Substring", in C. Iliopoulos et al. (Eds.): SPIRE 2015, LNCS 9309, pp. 246-257, 2015.

LINKS

Table of n, a(n) for n=1..18.

EXAMPLE

For n = 3 the longest unbordered subwords of 000,111 are of length 1; of 010,101 are of length 2; and for all others are of length 3.  So a(3) = 1+1+2+2+3+3+3+3 = 18.

CROSSREFS

Sequence in context: A217526 A018027 A218759 * A059413 A256828 A197055

Adjacent sequences:  A295496 A295497 A295498 * A295500 A295501 A295502

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Feb 17 2018

STATUS

approved

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Last modified August 18 22:29 EDT 2019. Contains 326109 sequences. (Running on oeis4.)