This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056283 #24 Sep 29 2018 00:01:18 %S A056283 0,0,2,9,30,91,258,729,2018,5613,15546,43315,120750,338259,950062, %T A056283 2678499,7573350,21480739,61088874,174184755,497812638,1425847623, %U A056283 4092087522,11765822365,33887517870,97756387365,282414624746,816999710223,2366509198350,6862930841141 %N A056283 Number of n-bead necklaces with exactly three different colored beads. %C A056283 Turning over the necklace is not allowed. %D A056283 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] %H A056283 Alois P. Heinz, <a href="/A056283/b056283.txt">Table of n, a(n) for n = 1..1000</a> %F A056283 a(n) = A001867(n) - 3*A000031(n) + 3. %F A056283 From _Robert A. Russell_, Sep 26 2018: (Start) %F A056283 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. %F A056283 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) %e A056283 For n=3, the two necklaces are ABC and ACB. %t A056283 k=3; Table[k!DivisorSum[n,EulerPhi[#]StirlingS2[n/#,k]&]/n,{n,1,30}] (* _Robert A. Russell_, Sep 26 2018 *) %Y A056283 Cf. A000031, A001867, A052823. %Y A056283 Column k=3 of A087854. %K A056283 nonn %O A056283 1,3 %A A056283 _Marks R. Nester_