Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jul 02 2018 15:35:51
%S 2,5,10,21,42,95,210,510,1258,3249,8538,23033,62778,173451,482690,
%T 1353075,3811362,10785233,30625194,87239997,249174234,713416599,
%U 2046945138,5884580072,16946835090,48883925865,141217957618,408519816609,1183291934298,3431535849811
%N "DIK" (bracelet, indistinct, unlabeled) transform of 2,2,2,2...
%H Andrew Howroyd, <a href="/A032283/b032283.txt">Table of n, a(n) for n = 1..200</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>
%F G.f.: (x*(2+3*x-x^2)/((1-x)*(1-3*x^2)) + Sum_{d>0} phi(d)*log((1-x^d)/(1-3*x^d))/d)/2. - _Andrew Howroyd_, Jun 20 2018
%t seq[n_] := (x*(2 + 3*x - x^2)/((1 - x)*(1 - 3*x^2)) + Sum[EulerPhi[d]*(Log[(1 - x^d)/(1 - 3*x^d)]/d), {d, 1, n}])/2 + O[x]^(n + 1) // CoefficientList[#, x]& // Rest;
%t seq[30] (* _Jean-François Alcover_, Jul 02 2018, after _Andrew Howroyd_ *)
%o (PARI) seq(n)={Vec(sum(d=1, n, eulerphi(d)/d*log((1-x^d)/(1-3*x^d) + O(x*x^n))) + x*(2+3*x-x^2)/((1-x)*(1-3*x^2)))/2} \\ _Andrew Howroyd_, Jun 20 2018
%K nonn
%O 1,1
%A _Christian G. Bower_
%E Terms a(28) and beyond from _Andrew Howroyd_, Jun 20 2018