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Search: id:A060165
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| A060165 |
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Number of orbits of length n under the map whose periodic points are counted by A000984. |
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+0
12
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| 2, 2, 6, 16, 50, 150, 490, 1600, 5400, 18450, 64130, 225264, 800046, 2865226, 10341150, 37566720, 137270954, 504171432, 1860277042, 6892317200, 25631327190, 95640829922, 357975249026, 1343650040256
(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 A000984 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 sequence A000984, 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(5) = 50 because if a map has A000984 as its periodic points, then it would have 2 fixed points and 252 points of period 5, hence 50 orbits of length 5.
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CROSSREFS
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Cf. A000984, A060164, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173.
a(n) = A022553(n)*2
Cf. A007727.
Sequence in context: A001464 A067136 A034439 this_sequence A134295 A062833 A006250
Adjacent sequences: A060162 A060163 A060164 this_sequence A060166 A060167 A060168
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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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