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A060164 Number of orbits of length n under the map whose periodic points are counted by A000364. 9
1, 2, 20, 345, 10104, 450450, 28480140, 2423938845, 267208852820, 37037118818700, 6304443126648900, 1292877846962865230, 314390193022547991720, 89447117243116404721950 (list; graph; refs; listen; history; text; internal format)



The sequence A000364 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.


Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.


Table of n, a(n) for n=1..14.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.


If a(n) is the n-th term of A000364, then the n-th term is u(n) = (1/n)* Sum_{d|n}\mu(d)a(n/d)


u(3) = 20 since the conjectured map whose periodic points are counted by A000364 would have 1 fixed point and 61 points of period 3, so it must have 20 orbits of length 3.


Cf. A000364, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173.

Sequence in context: A128481 A177397 A104462 * A084948 A187661 A218306

Adjacent sequences:  A060161 A060162 A060163 * A060165 A060166 A060167




Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001



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Last modified December 19 11:31 EST 2014. Contains 252213 sequences.