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A280303
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Number of binary necklaces of length n with no subsequence 00000.
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4
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1, 2, 3, 5, 7, 12, 17, 31, 51, 91, 155, 287, 505, 930, 1695, 3129, 5759, 10724, 19913, 37239, 69643, 130745, 245715, 463099, 873705, 1651838, 3126707, 5927817, 11251031, 21382558, 40679233, 77475673, 147694719, 281822847, 538213671, 1028714071, 1967728553
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of cyclic sequences of length n consisting of zeros and ones that do not contain five consecutive zeros provided we consider as equivalent those sequences that are cyclic shifts of each other.
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LINKS
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FORMULA
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a(n) = (1/n) * Sum_{d divides n} totient(n/d) * A074048(d).
G.f.: Sum_{k>=1} (phi(k)/k) * log(1/(1-B(x^k))) where B(x) = x*(1+x+x^2+x^3+x^4).
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EXAMPLE
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a(5)=7 because we have seven binary cyclic sequences (necklaces) of length 5 that avoid five consecutive zeros: 00001, 00011, 00101, 00111, 01101, 01111, 11111.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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