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A152061
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Counts of unique periodic binary strings of length n.
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14
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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
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OFFSET
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0,3
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COMMENTS
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a(p) = 2 for p prime.
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LINKS
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FORMULA
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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.
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EXAMPLE
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a(3) = 2 = |{ 000, 111 }|, a(4) = 4 = |{ 0000, 1111, 0101, 1010 }|.
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MAPLE
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with(numtheory):
a:= n-> `if`(n=0, 0, 2^n -add(mobius(n/d)*2^d, d=divisors(n))):
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MATHEMATICA
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a[0] = 0; a[n_] := 2^n - Sum[MoebiusMu[n/d]*2^d, {d, Divisors[n]}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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