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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, Mar 21 2001 EXTENSIONS More terms from Michel Marcus, Sep 11 2017 STATUS approved

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Last modified September 18 10:51 EDT 2021. Contains 347518 sequences. (Running on oeis4.)