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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056288 Number of primitive (period n) n-bead necklaces with exactly three different colored beads. 4
0, 0, 2, 9, 30, 89, 258, 720, 2016, 5583, 15546, 43215, 120750, 338001, 950030, 2677770, 7573350, 21478632, 61088874, 174179133, 497812378, 1425832077, 4092087522, 11765778330, 33887517840, 97756266615, 282414622728, 816999371955, 2366509198350, 6862929885407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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)*A056283(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, 3-j)*binomial(3, j)*(-1)^j, j=0..3):

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

CROSSREFS

Cf. A027376.

Column k=3 of A254040.

Sequence in context: A056778 A177111 A268586 * A261174 A273652 A056283

Adjacent sequences:  A056285 A056286 A056287 * A056289 A056290 A056291

KEYWORD

nonn

AUTHOR

Marks R. Nester (nesterm(AT)dpi.qld.gov.au)

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 July 23 14:53 EDT 2017. Contains 289688 sequences.