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A216215 Number of (weakly) superprimitive binary sequences of length n. 2
1, 2, 2, 6, 12, 28, 54, 118, 230, 490, 968, 1980, 3978, 8066, 16100, 32494, 64994, 130468, 261000, 523092, 1046292, 2094812, 4189704, 8383732, 16768206, 33545152, 67090578, 134199252, 268399910, 536834026, 1073671504, 2147411556, 4294826718, 8589792856, 17179592372, 34359455674 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A string x of length n is (strongly) quasiperiodic if there exists a string w of length < n such that x can be exactly covered by (possibly overlapping) occurrences of w in x. For example, 01001010 can be covered by 3 occurrences of 010. A string is (weakly) superprimitive if it is not strongly quasiperiodic.
LINKS
A. Apostolico, M. Farach, and C. S. Iliopoulos, Optimal superprimitivity testing for strings, Info. Proc. Letters 39 (1991), 17-20.
Rémy Sigrist, C program for A216215
EXAMPLE
a(4) = 12 because the 6 strings
0001,
0010,
0011,
0100,
0110,
0111
and their complements are the only weakly superprimitive strings of length 4.
PROG
(C) See Links section.
CROSSREFS
Cf. A216214.
Sequence in context: A035615 A115962 A019311 * A052994 A088219 A027375
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Mar 13 2013
EXTENSIONS
a(17)-a(35) from Rémy Sigrist, Jan 09 2019
STATUS
approved

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Last modified May 20 19:00 EDT 2024. Contains 372720 sequences. (Running on oeis4.)