OFFSET
1,3
COMMENTS
Old name was: A061694 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n under that map.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..200
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
Thomas Ward, Exactly realizable sequences. [local copy].
FORMULA
If b(n) is the n-th term of A061694, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).
a(n) ~ 3^(3*n + 1) / (8 * Pi^2 * n^3). - Vaclav Kotesovec, Sep 05 2019
EXAMPLE
b(1)=0, b(3)=36 so a(3)=12.
MATHEMATICA
Table[Sum[MoebiusMu[d] * Sum[Sum[((n/d)!/(i!*j!*(n/d - i - j)!))^3/6, {i, 1, n/d - j - 1}], {j, 1, n/d}], {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Sep 05 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ward, Feb 24 2004
EXTENSIONS
Name clarified by Michel Marcus, May 14 2015
STATUS
approved