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A060224 Number of orbits of length n under the map whose periodic points are counted by A047863. 0
2, 2, 8, 39, 288, 3046, 47232, 1061100, 34385064, 1601137110, 106806380544, 10186152828755, 1386394018652160, 268976332493883474, 74301040560350828856, 29201332000320392849280, 16315436194909017151242240, 12952804290011844088808158188, 14603450579455204338154338779136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 divides n } mu(d)*A047863(n/d).

EXAMPLE

a(5)=288 since the 6th term of A047863 is 1442 and the 2nd term is 2, so there must be (1442-2)/5 = 288 orbits of length 5.

PROG

(PARI) a047863(n) = n!*polcoeff(sum(k=0, n, exp(2^k*x +x*O(x^n))*x^k/k!), n);

a(n) = (1/n)*sumdiv(n, d, moebius(d)*a047863(n/d)); \\ Michel Marcus, Sep 11 2017

CROSSREFS

Cf. A047863.

Sequence in context: A009543 A102647 A318869 * A232980 A212307 A111605

Adjacent sequences:  A060221 A060222 A060223 * A060225 A060226 A060227

KEYWORD

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 19:01 EDT 2020. Contains 337265 sequences. (Running on oeis4.)