A332983 Number of length-n binary words closed by an unbordered word.

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

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: A336940 A291365 A154779 * A010101 A274942 A028408

Adjacent sequences: A332980 A332981 A332982 * A332984 A332985 A332986

Keyword

nonn

Author

Jeffrey Shallit, Mar 05 2020

Status

approved