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A060309 A001067 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. 0

%I #11 Nov 08 2022 23:33:50

%S 1,0,0,0,0,115,0,452,4874,17461,7062,19696950,50610,242341439,

%T 114877883680,481832564850,8919335150,1461959530725195586,

%U 8116326631140,13054135924822447372,72385602091336704890,115013510658268698717,1127506827209663824722

%N A001067 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 T. Ward, <a href="http://www.mth.uea.ac.uk/~h720/research/files/integersequences.html">Exactly realizable sequences</a>

%F If b(n) is the n-th term of A001067, then a(n)=(1/n)* |Sum_{d|n}mu(d)b(n/d)|, n<>2.

%e a(11) = 7062 because the 11th term of A001067 is 77683 and the first term is 1, so there should be (77683-1)/11 = 7062 orbits of length 11.

%Y Cf. A001067, A060171, A060479.

%K nonn

%O 1,6

%A _Thomas Ward_, Apr 10 2001

%E a(18) corrected and more terms from _Sean A. Irvine_, Nov 08 2022

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Last modified May 16 23:54 EDT 2024. Contains 372555 sequences. (Running on oeis4.)