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A060221 Number of orbits of length n under the full 18-shift (whose periodic points are counted by A001027). 1
18, 153, 1938, 26163, 377910, 5667681, 87460002, 1377481950, 22039920504, 357046533675, 5842582734474, 96402612275775, 1601766528128550, 26772383354990049, 449776041098370870, 7589970692848393200, 128583032925805678350, 2185911559727674682148, 37275544492386193492506 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of Lyndon words (aperiodic necklaces) with n beads of 18 colors. - Andrew Howroyd, Dec 10 2017

LINKS

Table of n, a(n) for n=1..19.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.

T. Ward, Exactly realizable sequences

FORMULA

a(n) = (1/n)* Sum_{d|n} mu(d)*A001027(n/d).

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 18*x^k))/k. - Ilya Gutkovskiy, May 20 2019

EXAMPLE

a(2)=153 since there are 324 points of period 2 in the full 18-shift and 18 fixed points, so there must be (324-18)/2 = 153 orbits of length 2.

PROG

(PARI) a001027(n) = 18^n;

a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001027(n/d)); \\ Michel Marcus, Sep 11 2017

CROSSREFS

Column 18 of A074650.

Cf. A001027.

Sequence in context: A047643 A010934 A022613 * A244876 A171741 A197239

Adjacent sequences:  A060218 A060219 A060220 * A060222 A060223 A060224

KEYWORD

easy,nonn

AUTHOR

Thomas Ward (t.ward(AT)uea.ac.uk), Mar 21 2001

EXTENSIONS

More terms from Michel Marcus, Sep 11 2017

STATUS

approved

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Last modified September 21 01:52 EDT 2020. Contains 337266 sequences. (Running on oeis4.)