|
%I #8 Feb 19 2021 20:10:00
%S 0,2,9,42,225,1260,7497,46176,293382,1908150,12655269,85287870,
%T 582628683,4026368514,28104231825,197884340160,1404038987577,
%U 10029929788566,72086075552493,520920674929650
%N Number of orbits of length n under the map whose periodic points are counted by A061693.
%C Old name was: A061693 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.
%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
%H Thomas Ward, <a href="http://web.archive.org/web/20081002082625/http://www.mth.uea.ac.uk/~h720/research/files/integersequences.html">Exactly realizable sequences</a>. <a href="/A091112/a091112.pdf">[local copy]</a>.
%F If b(n) is the n-th term of A061693, then a(n) = (1/n)*Sum_{d|n}mu(d)a(n/d).
%F a(n) ~ 8^n / (Pi*sqrt(3)*n^2). - _Vaclav Kotesovec_, Sep 05 2019
%e a(3)=9 since a(3)=(1/3)(b(3)-b(1)) where b is the sequence A061693, which starts 0,4,27.
%t Table[Sum[MoebiusMu[d] * (Sum[Binomial[n/d, k]^3, {k, 0, n/d}]/2 - 1), {d, Divisors[n]}]/n, {n, 1, 20}] (* _Vaclav Kotesovec_, Sep 05 2019 *)
%Y Cf. A061693.
%K nonn
%O 1,2
%A _Thomas Ward_, Feb 24 2004
%E Name clarified by _Michel Marcus_, May 14 2015
|
