A060221 Number of orbits of length n under the full 18-shift (whose periodic points are counted by A001027).

18, 153, 1938, 26163, 377910, 5667681, 87460002, 1377481950, 22039920504, 357046533675, 5842582734474, 96402612275775, 1601766528128550, 26772383354990049, 449776041098370870, 7589970692848393200, 128583032925805678350, 2185911559727674682148, 37275544492386193492506

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, Mar 21 2001

Extensions

More terms from Michel Marcus, Sep 11 2017

Status

approved