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Search: id:A060216
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| A060216 |
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Number of orbits of length n under the full 13-shift (whose periodic points are counted by A001022). |
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1
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| 13, 78, 728, 7098, 74256, 804076, 8964072, 101962770, 1178277464, 13785812040, 162923672184, 1941506688940, 23298085122480, 281241165925044, 3412392867581152, 41588538022965570
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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 A001022, 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)=78 since there are 169 points of period 2 in the full 13-shift and 13 fixed points, so there must be (169-13)/2 = 78 orbits of length 2.
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CROSSREFS
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Cf. A001022.
Sequence in context: A047638 A010929 A022608 this_sequence A041318 A142056 A081584
Adjacent sequences: A060213 A060214 A060215 this_sequence A060217 A060218 A060219
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KEYWORD
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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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