|
|
A060170
|
|
Number of orbits of length n under the map whose periodic points are counted by A005809.
|
|
12
|
|
|
3, 6, 27, 120, 600, 3078, 16611, 91872, 520749, 3004200, 17594247, 104304888, 624801957, 3775722342, 22991161500, 140928011136, 868886416866, 5384796881850, 33525472069563, 209592223788000, 1315211209630794, 8281053081282894, 52301607644921259, 331260902534858976, 2103541885645955625, 13389670112374830378
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The sequence A005809 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above.
a(n) is divisible by n (cf. A268617), 2*a(n) is divisible by n^2 (cf. A268618).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(3) = 27 since a map whose periodic points are counted by A005809 has 3 fixed points and 84 points of period 3, hence 27 orbits of length 3.
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d, d))/n; \\ Michel Marcus, Sep 10 2017
|
|
CROSSREFS
|
Cf. A005809, A060164, A060165, A060166, A060167, A060168, A060179, A060171, A060171, A060172, A060173.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|