login
The OEIS is supported by the many generous donors 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
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
MATHEMATICA
b[n_, k_] := b[n, k] = If[n==0, 1, DivisorSum[n, MoebiusMu[n/#]*k^#&]/n];
a[n_] := Sum[b[n, 3 - j]*Binomial[3, j]*(-1)^j, {j, 0, 3}];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jun 06 2018, after Alois P. Heinz *)
CROSSREFS
Cf. A027376.
Column k=3 of A254040.
Sequence in context: A177111 A290746 A268586 * A261174 A273652 A056283
KEYWORD
nonn
AUTHOR
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)