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Search: id:A060166
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| A060166 |
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Number of orbits of length n under the map whose periodic points are counted by A001641. |
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+0
10
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| 1, 1, 1, 2, 3, 4, 7, 10, 17, 26, 44, 68, 115, 184, 306, 500, 835, 1374, 2301, 3822, 6409, 10718, 18028, 30280, 51077, 86130, 145641
(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 A001641 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 A001641, 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) = 7 since a map whose periodic points are counted by A001641 would have 1 fixed point and 50 points of period 7, hence 7 orbits of length 7.
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CROSSREFS
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Cf. A001641, A060164, A060165, A060167, A060168, A060169, A060170, A060171, A060171.
Sequence in context: A082766 A082958 A166012 this_sequence A053634 A094863 A094862
Adjacent sequences: A060163 A060164 A060165 this_sequence A060167 A060168 A060169
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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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