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 A152061 Counts of unique periodic binary strings of length n. 12
 0, 0, 2, 2, 4, 2, 10, 2, 16, 8, 34, 2, 76, 2, 130, 38, 256, 2, 568, 2, 1036, 134, 2050, 2, 4336, 32, 8194, 512, 16396, 2, 33814, 2, 65536, 2054, 131074, 158, 266176, 2, 524290, 8198, 1048816, 2, 2113462, 2, 4194316, 33272, 8388610, 2, 16842496, 128, 33555424 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(p) = 2 for p prime. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 Achilles A. Beros, Bjørn Kjos-Hanssen, Daylan Kaui, The number of long words having a given automatic complexity*, 2018. FORMULA a(n) = 2^n - A001037(n) * n for n>0, a(0) = 0. a(n) = 2^n - A027375(n) for n>0, a(0) = 0. a(n) = 2^n - Sum_{d|n} mu(n/d) 2^d for n>0, a(0) = 0. a(n) = 2^n - A143324(n,2). a(n) = 2 * A178472(n) for n > 0. - Alois P. Heinz, Jul 04 2019 EXAMPLE a(3) = 2 = |{ 000, 111 }|, a(4) = 4 = |{ 0000, 1111, 0101, 1010 }|. MAPLE with(numtheory): a:= n-> `if`(n=0, 0, 2^n -add(mobius(n/d)*2^d, d=divisors(n))): seq(a(n), n=0..100);  # Alois P. Heinz, Sep 26 2011 MATHEMATICA a[0] = 0; a[n_] := 2^n - Sum[MoebiusMu[n/d]*2^d, {d, Divisors[n]}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 04 2019 *) CROSSREFS Row sums of A050870. A050871 is bisection (even part). - R. J. Mathar, Sep 24 2011 Cf. A008683, A178472. Sequence in context: A292786 A326486 A053204 * A103314 A306019 A194560 Adjacent sequences:  A152058 A152059 A152060 * A152062 A152063 A152064 KEYWORD nonn AUTHOR Jin S. Choi, Sep 24 2011 STATUS approved

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Last modified August 9 11:08 EDT 2020. Contains 336323 sequences. (Running on oeis4.)