OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..113
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.
MATHEMATICA
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
(Magma)
A047863:= func< n | (&+[Binomial(n, k)*2^(k*(n-k)): k in [0..n]]) >;
[A060224(n): n in [1..40]]; // G. C. Greubel, Nov 03 2024
(SageMath)
def A047863(n): return sum(binomial(n, k)*2^(k*(n-k)) for k in range(n+1))
[A060224(n) for n in range(1, 41)] # G. C. Greubel, Nov 03 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ward, Mar 21 2001
EXTENSIONS
More terms from Michel Marcus, Sep 11 2017
STATUS
approved