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Search: id:A060223
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| A060223 |
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Number of orbits of length n under the map whose periodic points are counted by A000670. |
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+0
2
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| 1, 1, 4, 18, 108, 778, 6756, 68220, 787472, 10224702, 147512052, 2340963570, 40527565260, 760095923082, 15352212731820, 332228417589720, 7668868648772700, 188085259069430744
(list; graph; listen)
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OFFSET
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1,3
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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 A000670, 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(5)=108 since the 6th term of A000670 is 541 and the 2nd term is 1, so there must be (541-1)/5 = 108 orbits of length 5.
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CROSSREFS
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Cf. A000670.
Sequence in context: A007711 A020114 A009597 this_sequence A144085 A003708 A000986
Adjacent sequences: A060220 A060221 A060222 this_sequence A060224 A060225 A060226
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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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