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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
OFFSET
1,1
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 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
KEYWORD
nonn
AUTHOR
Thomas Ward, Mar 21 2001
EXTENSIONS
More terms from Michel Marcus, Sep 11 2017
STATUS
approved