%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