A060220 Number of orbits of length n under the full 17-shift (whose periodic points are counted by A001026).

17, 136, 1632, 20808, 283968, 4022064, 58619808, 871959240, 13176430176, 201599248032, 3115626937056, 48551851084080, 761890617915840, 12026987582075856, 190828203433892736, 3041324491793194440, 48661191875666868480, 781282469552728498992, 12582759772902701307744

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 A361150

Adjacent sequences: A060217 A060218 A060219 * A060221 A060222 A060223

Keyword

easy,nonn

Author

Thomas Ward, Mar 21 2001

Extensions

More terms from Michel Marcus, Sep 11 2017

Status

approved