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 A056283 Number of n-bead necklaces with exactly three different colored beads. 7
 0, 0, 2, 9, 30, 91, 258, 729, 2018, 5613, 15546, 43315, 120750, 338259, 950062, 2678499, 7573350, 21480739, 61088874, 174184755, 497812638, 1425847623, 4092087522, 11765822365, 33887517870, 97756387365, 282414624746, 816999710223, 2366509198350, 6862930841141 (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 a(n) = A001867(n) - 3*A000031(n) + 3. From Robert A. Russell, Sep 26 2018: (Start) a(n) = (k!/n) Sum_{d|n} phi(d) S2(n/d,k), where k=3 is the number of colors and S2 is the Stirling subset number A008277. G.f.: -Sum_{d>0} (phi(d)/d) * Sum_{j} (-1)^(k-j) * C(k,j) * log(1-j x^d), where k=3 is the number of colors. (End) EXAMPLE For n=3, the two necklaces are ABC and ACB. MATHEMATICA k=3; Table[k!DivisorSum[n, EulerPhi[#]StirlingS2[n/#, k]&]/n, {n, 1, 30}] (* Robert A. Russell, Sep 26 2018 *) CROSSREFS Cf. A000031, A001867, A052823. Column k=3 of A087854. Sequence in context: A056288 A261174 A273652 * A192518 A277241 A201164 Adjacent sequences:  A056280 A056281 A056282 * A056284 A056285 A056286 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 11 15:30 EST 2018. Contains 318049 sequences. (Running on oeis4.)