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Search: id:A060170
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| A060170 |
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Number of orbits of length n under the map whose periodic points are counted by A005809 (shifted by one). |
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+0
10
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| 3, 6, 27, 120, 600, 3078, 16611, 91872, 520749, 3004200, 17594247, 104304888, 624801957, 3775722342, 22991161500, 140928011136, 868886416866, 5384796881850, 33525472069563, 209592223788000, 1315211209630794
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence A005809 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.
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REFERENCES
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Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
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LINKS
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Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
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If a(n) is the (n+1)-th term of A005809, then the n-th term is u(n) = (1/n)* Sum_{d|n}\mu(d)a(n/d)
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EXAMPLE
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u(3) = 27 since a map whose periodic points are counted by A005809 has 3 fixed points and 84 points of period 3, hence 27 orbits of length 3.
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CROSSREFS
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Cf. A005809, A060164, A060165, A060166, A060167, A060168, A060179, A060171, A060171, A060172, A060173.
Sequence in context: A034502 A023169 A083695 this_sequence A097678 A074894 A083675
Adjacent sequences: A060167 A060168 A060169 this_sequence A060171 A060172 A060173
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001
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