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 A032275 #48 May 05 2021 00:18:44
%S A032275 4,10,20,55,136,430,1300,4435,15084,53764,192700,704370,2589304,
%T A032275 9608050,35824240,134301715,505421344,1909209550,7234153420,
%U A032275 27489127708,104717491064,399827748310,1529763696820
%N A032275 Number of bracelets (turnover necklaces) of n beads of 4 colors.
%H A032275 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A032275 F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A032275 F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H A032275 M. Taniguchi, H. Du, and J. S. Lindsey, <a href="https://doi.org/10.1021/ci400175f">Enumeration of virtual libraries of combinatorial modular macrocyclic (bracelet, necklace) architectures and their linear counterparts</a>, Journal of Chemical Information and Modeling, 53 (2013), 2203-2216.
%H A032275 <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F A032275 "DIK" (bracelet, indistinct, unlabeled) transform of 4, 0, 0, 0, ...
%F A032275 Equals (A001868(n) + A056486(n)) / 2 = A001868(n) - A278640(n) = A278640(n) + A056486(n), for n>=1.
%F A032275 a(n) = A081720(n,4), n >= 4. - _Wolfdieter Lang_, Jun 03 2012
%F A032275 G.f.: (1 - Sum_{n>=1} phi(n)*log(1 - 4*x^n)/n + (1+4*x+6*x^2)/(1-4*x^2))/2. - _Herbert Kociemba_, Nov 02 2016
%F A032275 a(n) = (k^floor((n+1)/2) + k^ceiling((n+1)/2))/4 + (1/(2*n))* Sum_{d|n} phi(d)*k^(n/d), where k=4 is the maximum number of colors. - _Robert A. Russell_, Sep 24 2018
%F A032275 a(n) = (k^floor((n+1)/2) + k^ceiling((n+1)/2))/4 + (1/(2*n))*Sum_{i=1..n} k^gcd(n,i), where k=4 is the maximum number of colors. (See A075195 formulas.) - _Richard L. Ollerton_, May 04 2021
%e A032275 For n=2, the ten bracelets are AA, AB, AC, AD, BB, BC, BD, CC, CD, and DD. - _Robert A. Russell_, Sep 24 2018
%t A032275 mx=40;CoefficientList[Series[(1-Sum[ EulerPhi[n]*Log[1-4*x^n]/n,{n,mx}]+(1+4 x+6 x^2)/(1-4 x^2))/2,{x,0,mx}],x] (* _Herbert Kociemba_, Nov 02 2016 *)
%t A032275 k=4; Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/(2n) + (k^Floor[(n+1)/2] + k^Ceiling[(n+1)/2])/4, {n, 1, 30}] (* _Robert A. Russell_, Sep 24 2018 *)
%Y A032275 Column 4 of A051137.
%K A032275 nonn
%O A032275 1,1
%A A032275 _Christian G. Bower_