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A045677 Number of 2n-bead balanced binary necklaces which are equivalent to their complement, but not equivalent to their reverse and their reversed complement.

%I A045677 #18 Sep 13 2019 07:47:36
%S A045677 0,0,0,0,0,0,2,2,8,14,36,62,142,252,524,968,1928,3600,7044,13286,
%T A045677 25740,48916,94364,180314,347630,666996,1286712,2477342,4785824,
%U A045677 9240012,17880320,34604066,67078024,130085052,252583200,490722344,954313264
%N A045677 Number of 2n-bead balanced binary necklaces which are equivalent to their complement, but not equivalent to their reverse and their reversed complement.
%C A045677 The number of 2n-bead balanced binary necklaces which are equivalent to their complement is A000013(n) and those which are equivalent to their reverse, complement and reversed complement is A045674(n). - _Andrew Howroyd_, Sep 28 2017
%H A045677 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F A045677 a(n) = A000013(n) - A045674(n). - _Andrew Howroyd_, Sep 28 2017
%t A045677 A045674[n_] := A045674[n] = If[n == 0, 1, If[EvenQ[n], 2^(n/2 - 1) + A045674[n/2], 2^((n - 1)/2)]];
%t A045677 a[n_] := If[n == 0, 1, Sum[EulerPhi[2 d] 2^(n/d), {d, Divisors[n]}]/(2 n)] - A045674[n];
%t A045677 a /@ Range[0, 36] (* _Jean-François Alcover_, Sep 13 2019 *)
%Y A045677 Cf. A000013, A045674, A045675, A045676, A045678.
%K A045677 nonn
%O A045677 0,7
%A A045677 _David W. Wilson_