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A060222
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Number of orbits of length n under the full 19-shift (whose periodic points are counted by A001029).
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0
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19, 171, 2280, 32490, 495216, 7839780, 127695960, 2122929090, 35854187880, 613106378136, 10590023536200, 184442905990860, 3234844881712080, 57071906063500860, 1012075135324821024
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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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Table of n, a(n) for n=1..15.
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 A001029, 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)=171 since there are 361 points of period 2 in the full 19-shift and 19 fixed points, so there must be (361-19)/2 = 171 orbits of length 2.
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CROSSREFS
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Cf. A001029.
Sequence in context: A047644 A010935 A022614 * A041690 A217698 A172642
Adjacent sequences: A060219 A060220 A060221 * A060223 A060224 A060225
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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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STATUS
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approved
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