login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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. 398-402.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 06:57 EST 2016. Contains 278963 sequences.