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A056331
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Number of primitive (aperiodic) reversible string structures with n beads using a maximum of two different colors.
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3
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1, 1, 2, 4, 9, 16, 35, 66, 133, 261, 527, 1032, 2079, 4123, 8244, 16440, 32895, 65639, 131327, 262380, 524762, 1049071, 2098175, 4195230, 8390646, 16779231, 33558392, 67112892, 134225919, 268443306
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OFFSET
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1,3
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COMMENTS
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A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure.
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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a(n) = sum mu(d)*A005418(n/d) where d divides n.
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[#] (2^(n/#-2) + 2^(Floor[n/#/2]-1))&];
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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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