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A115114 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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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.

FORMULA

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.

EXAMPLE

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.

CROSSREFS

Cf. A000016, A006575.

Sequence in context: A051603 A094927 A024423 * A086209 A022490 A102952

Adjacent sequences:  A115111 A115112 A115113 * A115115 A115116 A115117

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

STATUS

approved

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Last modified September 15 20:57 EDT 2014. Contains 246789 sequences.