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A332983 Number of length-n binary words closed by an unbordered word. 0
0, 2, 2, 4, 6, 12, 18, 34, 54, 100, 170, 310, 542, 1000, 1786, 3292, 5990, 11100, 20434, 38102, 70858, 132912, 249290, 470300, 888158, 1684488, 3199258, 6095502, 11631550, 22249232, 42621834, 81804946, 157221374, 302632804, 583237734, 1125468466, 2174144774 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A word is unbordered if it has no nontrivial prefix that is a suffix.  A word x is closed by a word y if y has exactly two occurrences in x, one as a prefix, and one as a suffix.

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

For n = 5 the a(5) = 6 words counted are 01001, 01101, 01110, and their binary complements.

CROSSREFS

Counts a subset of A226452.

Sequence in context: A267610 A291365 A154779 * A010101 A274942 A028408

Adjacent sequences:  A332980 A332981 A332982 * A332984 A332985 A332986

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Mar 05 2020

STATUS

approved

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Last modified July 7 15:49 EDT 2020. Contains 335495 sequences. (Running on oeis4.)