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Search: id:A060171
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| A060171 |
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Number of orbits of length n under a map whose periodic points seem to be counted by A006953. |
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+0
12
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| 12, 54, 80, 30, 24, 5400, 0, 990, 1568, 636, 24, 2720, 0, 240, 5704, 510, 0, 3835776, 0, 26724, 3600, 108, 24, 89760, 0, 240, 1064, 120, 24, 113569300, 0, 510, 11752, 0, 264, 278281640
(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 A006953 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 A006953, 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) = 80 since a map whose periodic points are counted by A006953 has 12 fixed points and 252 points of period 3, hence 80 orbits of length 3.
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CROSSREFS
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Cf. A006953, A060164, A060165, A060166, A060167, A060168, A060169, A060170, A060172, A060173.
Adjacent sequences: A060168 A060169 A060170 this_sequence A060172 A060173 A060174
Sequence in context: A045219 A054410 A030182 this_sequence A133078 A034436 A000735
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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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