A216214 - OEIS

A216214

Number of (strongly) superprimitive binary sequences of length n.

1, 2, 2, 4, 6, 8, 16, 24, 46, 84, 160, 300, 588, 1136, 2236, 4388, 8690

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

A string x of length n is (weakly) quasiperiodic if there is a string w of length < n for which copies can be placed (possibly overlapping; possibly hanging off the left and right ends of x) that completely cover x. For example, x = 001101 is weakly quasiperiodic with quasiperiod w = 0110; three copies of w suffice to cover x. A string is (strongly) superprimitive if it is not weakly quasiperiodic.

LINKS

Table of n, a(n) for n=0..16.

A. Apostolico, M. Farach, and C. S. Iliopoulos, Optimal superprimitivity testing for strings, Info. Proc. Letters 39 (1991), 17-20.

EXAMPLE

a(6) = 16 because the 8 strings

000001,

000011,

000101,

000111,

001011,

001111,

010111,