A060222 Number of orbits of length n under the full 19-shift (whose periodic points are counted by A001029).

19, 171, 2280, 32490, 495216, 7839780, 127695960, 2122929090, 35854187880, 613106378136, 10590023536200, 184442905990860, 3234844881712080, 57071906063500860, 1012075135324821024, 18027588346914850290, 322375697516753069760, 5784852794310472599780, 104127350297911241532840

Offset

1,1

Comments

Number of monic irreducible polynomials of degree n over GF(19). - Andrew Howroyd, Dec 10 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..799

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)*A001029(n/d).

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 19*x^k))/k. - Ilya Gutkovskiy, May 20 2019

Example

a(2)=171 since there are 361 points of period 2 in the full 19-shift and 19 fixed points, so there must be (361-19)/2 = 171 orbits of length 2.

Mathematica

a[n_]:=(1/n) Sum[MoebiusMu[d] 19^(n/d), {d, Divisors[n]}]; Table[a[n], {n, 20}] (* Vincenzo Librandi, Sep 19 2017 *)

Prog

(PARI) a001029(n) = 19^n;
a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001029(n/d)); \\ Michel Marcus, Sep 11 2017

Crossrefs

Column 19 of A074650.

Cf. A001029.

Sequence in context: A282288 A022614 A322878 * A041690 A217698 A172642

Adjacent sequences: A060219 A060220 A060221 * A060223 A060224 A060225

Keyword

easy,nonn

Author

Thomas Ward, Mar 21 2001

Extensions

More terms from Michel Marcus, Sep 11 2017

Status

approved