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A115115
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Number of 3-asymmetric rhythm cycles: binary necklaces of length 3n subject to the restriction that for any k if the k-th bead is of color 1 then the (k+n)-th and (k+2n)-th beads (modulo 3n) are of color 0.
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1
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2, 4, 8, 24, 70, 232, 782, 2744, 9710, 34990, 127102, 466152, 1720742, 6391714, 23860936, 89479864, 336860182, 1272587758, 4822419422, 18325211326, 69810262088, 266548336954, 1019836872142, 3909374909672, 15011998757958
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| 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
| a(n)=(Sum_{d|n}phi(3d)+Sum_{d|n, (3, d)=1}phi(d)4^(n/d))/(3n), where phi(n) is the Euler function A000010.
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CROSSREFS
| Cf. A115114.
Sequence in context: A078223 A116719 A114900 * A026097 A067646 A152875
Adjacent sequences: A115112 A115113 A115114 * A115116 A115117 A115118
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KEYWORD
| easy,nonn
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AUTHOR
| Valery A. Liskovets (liskov(AT)im.bas-net.by), Jan 17 2006
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