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Search: id:A060173
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| A060173 |
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Number of orbits of length n under a map whose periodic points are counted by A056045. |
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+0
7
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| 1, 1, 1, 2, 1, 6, 1, 12, 10, 30, 1, 139, 1, 252, 231, 920, 1, 3780, 1, 10250, 5601, 32076, 1, 149390, 2126, 400036, 173692, 1475642, 1, 6196651, 1, 19113136, 5864915, 68635494, 201405, 289525026, 1
(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 A056045 records 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 A056045, 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) = 1 since the map whose periodic points are counted by A056045 has 1 fixed point and 8 points of period 7, hence 1 orbits of length 7.
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CROSSREFS
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Cf. A056045, A060164, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172.
Adjacent sequences: A060170 A060171 A060172 this_sequence A060174 A060175 A060176
Sequence in context: A107754 A139625 A053785 this_sequence A059344 A109193 A083720
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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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