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Search: id:A060172
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| A060172 |
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Number of orbits of length n under a map whose periodic points are counted by A027306. |
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+0
7
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| 1, 1, 1, 2, 3, 6, 9, 19, 28, 62, 93, 205, 315, 703, 1091, 2440, 3855, 8616, 13797, 30801, 49929, 111311, 182361, 405751, 671088, 1490409, 2485504, 5509504, 9256395, 20480421, 34636833, 76499520
(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 A027306 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 A027306, 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) = 9 since the map whose periodic points are counted by A027306 has 1 fixed point and 64 points of period 7, hence 9 orbits of length 7.
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CROSSREFS
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Cf. A027306, A060164, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060173.
Sequence in context: A018679 A018741 A011962 this_sequence A003243 A055873 A091053
Adjacent sequences: A060169 A060170 A060171 this_sequence A060173 A060174 A060175
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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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