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Search: id:A060164
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| A060164 |
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Number of orbits of length n under the map whose periodic points are counted by A000364. |
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+0
10
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| 1, 2, 20, 345, 10104, 450450, 28480140, 2423938845, 267208852820, 37037118818700, 6304443126648900, 1292877846962865230, 314390193022547991720, 89447117243116404721950
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence A000364 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 A000364, 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) = 20 since the conjectured map whose periodic points are counted by A000364 would have 1 fixed point and 61 points of period 3, so it must have 20 orbits of length 3.
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CROSSREFS
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Cf. A000364, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173.
Sequence in context: A124211 A128481 A104462 this_sequence A084948 A009236 A078698
Adjacent sequences: A060161 A060162 A060163 this_sequence A060165 A060166 A060167
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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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