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%I #16 Dec 14 2017 21:15:49
%S 0,0,0,1,2,6,12,27,54,113,228,465,934,1890,3798,7644,15350,30840,
%T 61878,124173,249008,499318,1000866,2005971,4019446,8053062,16131780,
%U 32311665,64711820,129589530,259487040,519552495,1040186358,2082408354
%N Number of orientable necklaces with 2n beads and two colors which when turned over produce their own color complement.
%C Clearly in each necklace the number of beads of each of the two colors must be equal and so the number of beads must be even, if a(n) is to be positive.
%H G. C. Greubel, <a href="/A059078/b059078.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/A059078/a059078.gif">Illustration of initial terms</a>
%F a(n) = A059076(2*n) - 2*A059053(2*n).
%F a(n) = A000029(2*n) - A000013(2*n) - A000079(n-1).
%t a13[n_] := DivisorSum[n, EulerPhi@(2*#)*2^(n/#)&]/(2*n);
%t a29[n_] := (1/4)*(Mod[n, 2] + 3)*2^Quotient[n, 2] + DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2*n);
%t a[0] = 0; a[n_] := a29[2*n] - a13[2*n] - 2^(n - 1);
%t Array[a, 34, 0] (* _Jean-François Alcover_, Nov 05 2017 *)
%K nonn
%O 0,5
%A _Henry Bottomley_, Dec 22 2000
%E More terms from _Vladeta Jovovic_, Mar 06 2001
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