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Search: id:A060168
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| A060168 |
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Number of orbits of length n under the map whose periodic points are counted by A001643. |
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10
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| 1, 1, 1, 2, 4, 6, 10, 15, 26, 42, 74, 121, 212, 357, 620, 1064, 1856, 3209, 5618, 9794, 17192, 30153, 53114, 93554, 165308, 292250
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The sequence A001643 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.
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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-th term of A001643, then the n-th term is u(n) = (1/n)* Sum_{ d divides n }\mu(d)a(n/d)
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EXAMPLE
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u(7) = 10 since a map whose periodic points are counted by A001643 would have 1 fixed point and 71 points of period 7, hence 10 orbits of length 7.
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CROSSREFS
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Cf. A001642, A060164, A060165, A060166, A060167, A060169, A060170, A060171, A060171.
Sequence in context: A108925 A120549 A167270 this_sequence A113117 A134682 A083814
Adjacent sequences: A060165 A060166 A060167 this_sequence A060169 A060170 A060171
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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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