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 A060166 Number of orbits of length n under the map whose periodic points are counted by A001641. 9
 1, 1, 1, 2, 3, 4, 7, 10, 17, 26, 44, 68, 115, 184, 306, 500, 835, 1374, 2301, 3822, 6409, 10718, 18028, 30280, 51077, 86130, 145641 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The sequence A001641 seems to record the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above. REFERENCES Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402. LINKS Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. FORMULA If a(n) is the n-th term of A001641, then the n-th term is u(n) = (1/n)* Sum_{ d divides n }\mu(d)a(n/d) EXAMPLE u(7) = 7 since a map whose periodic points are counted by A001641 would have 1 fixed point and 50 points of period 7, hence 7 orbits of length 7. CROSSREFS Cf. A001641, A060164, A060165, A060167, A060168, A060169, A060170, A060171, A060171. Sequence in context: A082958 A218495 A166012 * A053634 A094863 A094862 Adjacent sequences:  A060163 A060164 A060165 * A060167 A060168 A060169 KEYWORD easy,nonn AUTHOR Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001 STATUS approved

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