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A060169
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Number of orbits of length n under the automorphism of the 3-torus whose periodic points are counted by A001945.
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8
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1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 4, 4, 5, 8, 6, 12, 13, 16, 23, 26, 35, 46, 54, 76, 89, 120, 154, 192, 255, 322, 411, 544, 679, 898, 1145, 1476, 1925, 2466, 3201, 4156, 5338, 6978, 8985
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| The sequence A001945 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above.
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REFERENCES
| Manfred Einsiedler, Graham Everest and Thomas Ward: Primes in sequences associated to polynomials (after Lehmer). LMS J. Comput. Math. 3 (2000), 125-139.
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
| Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
| If a(n) is the n-th term of A001945, then the n-th term is u(n) = (1/n)* Sum_{ d divides n }\mu(d)a(n/d)
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EXAMPLE
| u(17) = 8 since the map whose periodic points are counted by A001945 has 1 fixed point and 137 points of period 17, hence 8 orbits of length 7.
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CROSSREFS
| Cf. A001642, A060164, A060165, A060166, A060167, A060168, A060170, A060171, A060171, A060172, A060173.
Sequence in context: A159805 A009213 A072209 * A117958 A113401 A071227
Adjacent sequences: A060166 A060167 A060168 * A060170 A060171 A060172
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KEYWORD
| easy,nonn
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AUTHOR
| Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001
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