

A216214


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


1



1, 2, 2, 4, 6, 8, 16, 24, 46, 84, 160, 300, 588, 1136, 2236, 4388, 8690
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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), 1720.


EXAMPLE

a(6) = 16 because the 8 strings
000001,
000011,
000101,
000111,
001011,
001111,
010111,
011111
and their complements are strongly superprimitive.


CROSSREFS

Sequence in context: A255710 A239851 A153958 * A269298 A153964 A001010
Adjacent sequences: A216211 A216212 A216213 * A216215 A216216 A216217


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Mar 13 2013


STATUS

approved



