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A060218 Number of orbits of length n under the full 15-shift (whose periodic points are counted by A001024). 2
15, 105, 1120, 12600, 151872, 1897840, 24408480, 320355000, 4271484000, 57664963104, 786341441760, 10812193870800, 149707312950720, 2085208989609360, 29192926025339776, 410525522071875000, 5795654431511374080, 82105104444274758000, 1166756747396368729440, 16626283650369421872480 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Number of Lyndon words (aperiodic necklaces) with n beads of 15 colors. - Andrew Howroyd, Dec 10 2017
LINKS
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.
FORMULA
a(n) = (1/n)* Sum_{d|n} mu(d)*A001024(n/d).
G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 15*x^k))/k. - Ilya Gutkovskiy, May 19 2019
EXAMPLE
a(2)=105 since there are 225 points of period 2 in the full 15-shift and 15 fixed points, so there must be (225-15)/2 = 105 orbits of length 2.
MAPLE
f:= n -> 1/n*add(numtheory:-mobius(d)*15^(n/d), d = numtheory:-divisors(n)):
map(f, [$1..30]); # Robert Israel, Oct 28 2018
PROG
(PARI) a001024(n) = 15^n;
a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001024(n/d)); \\ Michel Marcus, Sep 11 2017
CROSSREFS
Column 15 of A074650.
Cf. A001024.
Sequence in context: A200852 A266503 A058085 * A226109 A264415 A319588
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 March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)