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Search: id:A060218
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| A060218 |
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Number of orbits of length n under the full 15-shift (whose periodic points are counted by A001024). |
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1
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| 15, 105, 1120, 12600, 151872, 1897840, 24408480, 320355000, 4271484000, 57664963104, 786341441760, 10812193870800, 149707312950720, 2085208989609360, 29192926025339776, 410525522071875000
(list; graph; listen)
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OFFSET
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1,1
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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.
T. Ward, Exactly realizable sequences
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FORMULA
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If b(n) is the (n+1)-th term of A001024, then the n-th term is a(n) = (1/n)* Sum_{d|n}\mu(d)b(n/d)
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EXAMPLE
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a(2)=105 since there are 225 points of period 2 in the full 15-shift and 15 fixed points, so there must be (225-15)/2 = 105 orbits of length 2.
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CROSSREFS
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Cf. A001024.
Sequence in context: A000478 A055848 A058085 this_sequence A165892 A077261 A012507
Adjacent sequences: A060215 A060216 A060217 this_sequence A060219 A060220 A060221
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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 21 2001
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