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A045676 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, but not equivalent to their complement and reversed complement.

%I A045676 #18 Sep 13 2019 08:02:15
%S A045676 0,0,0,0,2,2,14,12,58,54,232,220,886,860,3360,3304,12730,12614,48348,
%T A045676 48108,184224,183732,704376,703384,2702070,2700060,10396440,10392408,
%U A045676 40108336,40100216,155101008,155084752,601047482,601014854,2333540428
%N A045676 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, but not equivalent to their complement and reversed complement.
%C A045676 The number of 2n-bead balanced binary necklaces equivalent to their reverse is A128014(n) and those equivalent to their reverse, complement and reversed complement is A045674(n). - _Andrew Howroyd_, Sep 28 2017
%H A045676 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F A045676 a(n) = A128014(n) - A045674(n). - _Andrew Howroyd_, Sep 28 2017
%t A045676 A045674[n_] := A045674[n] = If[n == 0, 1, If[EvenQ[n], 2^(n/2 - 1) + A045674[n/2], 2^((n-1)/2)]];
%t A045676 a[n_] := SeriesCoefficient[(1+x)/Sqrt[1 - 4 x^2], {x, 0, n}] - A045674[n];
%t A045676 a /@ Range[0, 34] (* _Jean-François Alcover_, Sep 13 2019 *)
%Y A045676 Cf. A045674, A045675, A045677, A045678, A128014.
%K A045676 nonn
%O A045676 0,5
%A A045676 _David W. Wilson_