%I A060173
%S A060173 1,1,1,2,1,6,1,12,10,30,1,139,1,252,231,920,1,3780,1,10250,5601,32076,
%T A060173 1,149390,2126,400036,173692,1475642,1,6196651,1,19113136,5864915,
%U A060173 68635494,201405,289525026,1
%N A060173 Number of orbits of length n under a map whose periodic points are counted 
               by A056045.
%C A060173 The sequence A056045 records the number of points of period n under a 
               map. The number of orbits of length n for this map gives the sequence 
               above.
%D A060173 Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, 
               Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
%H A060173 Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">Arithmetic and growth of periodic orbits</a>, J. Integer 
               Seqs., Vol. 4 (2001), #01.2.1.
%F A060173 If a(n) is the n-th term of A056045, then the n-th term is u(n) = (1/
               n)* Sum_{ d divides n }\mu(d)a(n/d)
%e A060173 u(7) = 1 since the map whose periodic points are counted by A056045 has 
               1 fixed point and 8 points of period 7, hence 1 orbits of length 
               7.
%Y A060173 Cf. A056045, A060164, A060165, A060166, A060167, A060168, A060169, A060170, 
               A060171, A060172.
%Y A060173 Sequence in context: A107754 A139625 A053785 this_sequence A059344 A109193 
               A083720
%Y A060173 Adjacent sequences: A060170 A060171 A060172 this_sequence A060174 A060175 
               A060176
%K A060173 easy,nonn
%O A060173 1,4
%A A060173 Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001