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Search: id:A060221
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| A060221 |
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Number of orbits of length n under the full 18-shift (whose periodic points are counted by A001027). |
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+0
1
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| 18, 153, 1938, 26163, 377910, 5667681, 87460002, 1377481950, 22039920504, 357046533675, 5842582734474, 96402612275775, 1601766528128550, 26772383354990049, 449776041098370870
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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 A001027, 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)=153 since there are 324 points of period 2 in the full 18-shift and 18 fixed points, so there must be (324-18)/2 = 153 orbits of length 2.
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CROSSREFS
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Cf. A001027.
Sequence in context: A047643 A010934 A022613 this_sequence A171741 A060932 A119004
Adjacent sequences: A060218 A060219 A060220 this_sequence A060222 A060223 A060224
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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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