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%I #22 Feb 19 2021 20:10:00
%S 16,120,1360,16320,209712,2795480,38347920,536862720,7635496960,
%T 109951057896,1599289640400,23456246655680,346430740566960,
%U 5146970983535160,76861433640386288,1152921504338411520
%N Number of orbits of length n under the full 16-shift (whose periodic points are counted by A001025).
%C Number of monic irreducible polynomials of degree n over GF(16). - _Robert Israel_, Jan 07 2015
%C Number of Lyndon words (aperiodic necklaces) with n beads of 16 colors. - _Andrew Howroyd_, Dec 10 2017
%H Yash Puri and Thomas Ward, <a href="http://www.fq.math.ca/Scanned/39-5/puri.pdf">A dynamical property unique to the Lucas sequence</a>, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H T. Ward, <a href="http://www.mth.uea.ac.uk/~h720/research/files/integersequences.html">Exactly realizable sequences</a>
%F a(n) = (1/n)* Sum_{d|n} mu(d)*16^(n/d).
%F G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 16*x^k))/k. - _Ilya Gutkovskiy_, May 19 2019
%e a(2)=120 since there are 256 points of period 2 in the full 16-shift and 16 fixed points, so there must be (256-16)/2 = 120 orbits of length 2.
%p f:= (n,p) -> add(numtheory:-mobius(d)*p^(n/d),d=numtheory:-divisors(n))/n:
%p seq(f(n,16),n=1..30); # _Robert Israel_, Jan 07 2015
%o (PARI) a(n) = sumdiv(n, d, moebius(d)*16^(n/d))/n; \\ _Michel Marcus_, Jan 07 2015
%Y Column 16 of A074650.
%Y Cf. A001025.
%K easy,nonn
%O 1,1
%A _Thomas Ward_, Mar 21 2001
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