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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

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

Adjacent sequences:  A056285 A056286 A056287 * A056289 A056290 A056291

KEYWORD

nonn

AUTHOR

Marks R. Nester

STATUS

approved

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Last modified December 11 15:53 EST 2018. Contains 318049 sequences. (Running on oeis4.)