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A115116 Number of imprimitive (periodic) asymmetric rhythm cycles: ones having nontrivial shift automorphisms. Asymmetric rhythm cycles (A115114): 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. 0
1, 1, 2, 1, 2, 3, 2, 1, 6, 3, 2, 11, 2, 3, 30, 1, 2, 63, 2, 11, 162, 3, 2, 411, 26, 3, 1098, 11, 2, 3015, 2, 1, 8058, 3, 182, 22151, 2, 3, 61326, 411, 2, 170883, 2, 11, 479410, 3, 2, 1345211, 158, 2955, 3798246, 11, 2, 10761723, 8078, 411, 30585834, 3, 2, 87191759 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(2^k)=1 for all k including k=0. a(p)=2, a(2p)=3, a(4p)=11, etc. for an odd prime p.

LINKS

Table of n, a(n) for n=1..60.

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)=A115114(n) - A006575(n).

CROSSREFS

Sequence in context: A128979 A190167 A171565 * A141662 A088062 A248886

Adjacent sequences:  A115113 A115114 A115115 * A115117 A115118 A115119

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

STATUS

approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)