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A060222 Number of orbits of length n under the full 19-shift (whose periodic points are counted by A001029). 2
19, 171, 2280, 32490, 495216, 7839780, 127695960, 2122929090, 35854187880, 613106378136, 10590023536200, 184442905990860, 3234844881712080, 57071906063500860, 1012075135324821024, 18027588346914850290, 322375697516753069760, 5784852794310472599780, 104127350297911241532840 (list; graph; refs; listen; history; text; internal format)
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 (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 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)