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A115114
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Asymmetric rhythm cycles (patterns): binary necklaces of length 2n subject to the restriction that for any k if the k-th bead is of color 1 then the (k+n)-th bead (modulo 2n) is of color 0.
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3
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2, 3, 6, 11, 26, 63, 158, 411, 1098, 2955, 8054, 22151, 61322, 170823, 478318, 1345211, 3798242, 10761723, 30585830, 87169619, 249056138, 713205903, 2046590846, 5883948951, 16945772210, 48882035163, 141214768974
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..27.
R. W. Hall and P. Klingsberg, Asymmetric Rhythms, Tiling Canons and Burnside's Lemma,Bridges Proceedings, pp. 189-194, 2004 (Winfield, Kansas).
R. W. Hall and P. Klingsberg, Asymmetric Rhythms and Tiling Canons, Preprint, 2004.
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FORMULA
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a(n)=(Sum_{d|n}phi(2d)+Sum_{d|n, d odd}phi(d)3^(n/d))/(2n), where phi(n) is the Euler function A000010.
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EXAMPLE
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For n=3, the 27=3^3 admissible words are separated into 6 shift-equivalence classes (necklaces) containing, resp., the words 000000, 100000, 110000, 101000, 111000 and 101010. Thus a(3)=6.
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CROSSREFS
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Cf. A000016, A006575.
Sequence in context: A051603 A094927 A024423 * A086209 A022490 A102952
Adjacent sequences: A115111 A115112 A115113 * A115115 A115116 A115117
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KEYWORD
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easy,nonn
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AUTHOR
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Valery A. Liskovets, Jan 17 2006
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STATUS
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approved
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