A060217 Number of orbits of length n under the full 14-shift (whose periodic points are counted by A001023).

14, 91, 910, 9555, 107562, 1254435, 15059070, 184468830, 2295671560, 28925411697, 368142288150, 4724492067295, 61054982558010, 793714765724595, 10371206370484778, 136122083520848880, 1793608631137129170, 23715491899442676060, 314542313628890231430, 4183412771249777343369

Offset

1,1

Comments

Number of Lyndon words (aperiodic necklaces) with n beads of 14 colors. - Andrew Howroyd, Dec 10 2017

Links

Table of n, a(n) for n=1..20.

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)*A001023(n/d).

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 14*x^k))/k. - Ilya Gutkovskiy, May 19 2019

Example

a(2)=91 since there are 196 points of period 2 in the full 14-shift and 14 fixed points, so there must be (196-14)/2 = 91 orbits of length 2.

Prog

(PARI) a001023(n) = 14^n;
a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001023(n/d)); \\ Michel Marcus, Sep 11 2017

Crossrefs

Column 14 of A074650.

Cf. A001023.

Sequence in context: A010930 A220892 A022609 * A113776 A202901 A224328

Adjacent sequences: A060214 A060215 A060216 * A060218 A060219 A060220

Keyword

easy,nonn

Author

Thomas Ward, Mar 21 2001

Extensions

More terms from Michel Marcus, Sep 11 2017

Status

approved