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A115115 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. 1
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; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..25.

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.

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.

CROSSREFS

Cf. A115114.

Sequence in context: A231721 A114900 A264570 * A026097 A264557 A067646

Adjacent sequences:  A115112 A115113 A115114 * A115116 A115117 A115118

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)