

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
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OFFSET

1,2


COMMENTS

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.


REFERENCES

Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398402.


LINKS

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.


FORMULA

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


EXAMPLE

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.


CROSSREFS

Cf. A000364, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173.
Sequence in context: A128481 A177397 A104462 * A267827 A084948 A187661
Adjacent sequences: A060161 A060162 A060163 * A060165 A060166 A060167


KEYWORD

easy,nonn


AUTHOR

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


STATUS

approved



