A060164 Number of orbits of length n under the map whose periodic points are counted by A000364.

1, 2, 20, 345, 10104, 450450, 28480140, 2423938845, 267208852820, 37037118818700, 6304443126648900, 1292877846962865230, 314390193022547991720, 89447117243116404721950, 29436259549934873636908816, 11094961973721205588579579845, 4748429366816935180127543967840

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..243

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

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

Formula

a(n) = (1/n)* Sum_{d|n} mu(d)*A000364(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: A304861 A104462 A352601 * A267827 A084948 A187661

Adjacent sequences: A060161 A060162 A060163 * A060165 A060166 A060167

Keyword

easy,nonn

Author

Thomas Ward, Mar 13 2001

Status

approved