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Search: id:A060167
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| A060167 |
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Number of orbits of length n under the map whose periodic points are counted by A001642. |
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10
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| 1, 1, 1, 2, 4, 5, 9, 13, 23, 36, 63, 101, 175, 290, 497, 840, 1445, 2460, 4247, 7293, 12619, 21805, 37856, 65695, 114401, 199280, 347944
(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 A001642 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 A001642, 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 a map whose periodic points are counted by A001642 would have 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. A001642, A060164, A060165, A060166, A060168, A060169, A060170, A060171, A060171.
Sequence in context: A060312 A068372 A068370 this_sequence A118550 A126697 A162406
Adjacent sequences: A060164 A060165 A060166 this_sequence A060168 A060169 A060170
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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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