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A060220 Number of orbits of length n under the full 17-shift (whose periodic points are counted by A001026). 1
17, 136, 1632, 20808, 283968, 4022064, 58619808, 871959240, 13176430176, 201599248032, 3115626937056, 48551851084080, 761890617915840, 12026987582075856, 190828203433892736, 3041324491793194440, 48661191875666868480, 781282469552728498992, 12582759772902701307744 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of monic irreducible polynomials of degree n over GF(17). - 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)*A001026(n/d).

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 17*x^k))/k. - Ilya Gutkovskiy, May 20 2019

EXAMPLE

a(2)=136 since there are 289 points of period 2 in the full 17-shift and 17 fixed points, so there must be (289-17)/2 = 136 orbits of length 2.

PROG

(PARI) a001024(n) = 17^n;

a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001024(n/d)); \\ Michel Marcus, Sep 11 2017

CROSSREFS

Column 17 of A074650.

Cf. A001026.

Sequence in context: A010933 A022612 A205815 * A041550 A142788 A244874

Adjacent sequences:  A060217 A060218 A060219 * A060221 A060222 A060223

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 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)