Search: id:A060167
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%I A060167
%S A060167 1,1,1,2,4,5,9,13,23,36,63,101,175,290,497,840,1445,2460,4247,7293,
%T A060167 12619,21805,37856,65695,114401,199280,347944
%N A060167 Number of orbits of length n under the map whose periodic points are 
               counted by A001642.
%C A060167 The sequence A001642 seems to record 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 A060167 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 A060167 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 A060167 If a(n) is the n-th term of A001642, then the n-th term is u(n) = (1/
               n)* Sum_{ d divides n }\mu(d)a(n/d)
%e A060167 u(7) = 9 since a map whose periodic points are counted by A001642 would 
               have 1 fixed point and 64 points of period 7, hence 9 orbits of length 
               7.
%Y A060167 Cf. A001642, A060164, A060165, A060166, A060168, A060169, A060170, A060171, 
               A060171.
%Y A060167 Sequence in context: A060312 A068372 A068370 this_sequence A118550 A126697 
               A162406
%Y A060167 Adjacent sequences: A060164 A060165 A060166 this_sequence A060168 A060169 
               A060170
%K A060167 easy,nonn
%O A060167 1,4
%A A060167 Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001

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