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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 (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
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,
011111
and their complements are strongly superprimitive.
CROSSREFS
Sequence in context: A329137 A239851 A153958 * A269298 A153964 A001010
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Mar 13 2013
STATUS
approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)