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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056290 Number of primitive (period n) n-bead necklaces with exactly five different colored beads. 4
0, 0, 0, 0, 24, 300, 2400, 15750, 92680, 510288, 2691600, 13793850, 69309240, 343499100, 1686135352, 8221421250, 39901776360, 193053923860, 932142850800, 4495236287850, 21664357532920, 104388118174500, 503044634004000, 2425003910574000, 11696087875731600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Turning over the necklace is not allowed.

REFERENCES

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

sum mu(d)*A056285(n/d) where d|n.

MAPLE

with(numtheory):

b:= proc(n, k) option remember; `if`(n=0, 1,

      add(mobius(n/d)*k^d, d=divisors(n))/n)

    end:

a:= n-> add(b(n, 5-j)*binomial(5, j)*(-1)^j, j=0..5):

seq(a(n), n=1..30);  # Alois P. Heinz, Jan 25 2015

MATHEMATICA

b[n_, k_] := b[n, k] = If[n==0, 1, DivisorSum[n, MoebiusMu[n/#]*k^# &]/n];

a[n_] := Sum[b[n, 5 - j]*Binomial[5, j]*(-1)^j, {j, 0, 5}];

Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jun 06 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A001692.

Column k=5 of A254040.

Sequence in context: A162366 A153782 A073990 * A056285 A162686 A010976

Adjacent sequences:  A056287 A056288 A056289 * A056291 A056292 A056293

KEYWORD

nonn

AUTHOR

Marks R. Nester

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 15:03 EST 2018. Contains 318049 sequences. (Running on oeis4.)