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

%I #18 Sep 13 2019 08:02:15

%S 0,0,0,0,2,2,14,12,58,54,232,220,886,860,3360,3304,12730,12614,48348,

%T 48108,184224,183732,704376,703384,2702070,2700060,10396440,10392408,

%U 40108336,40100216,155101008,155084752,601047482,601014854,2333540428

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

%C 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 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>

%F a(n) = A128014(n) - A045674(n). - _Andrew Howroyd_, Sep 28 2017

%t A045674[n_] := A045674[n] = If[n == 0, 1, If[EvenQ[n], 2^(n/2 - 1) + A045674[n/2], 2^((n-1)/2)]];

%t a[n_] := SeriesCoefficient[(1+x)/Sqrt[1 - 4 x^2], {x, 0, n}] - A045674[n];

%t a /@ Range[0, 34] (* _Jean-François Alcover_, Sep 13 2019 *)

%Y Cf. A045674, A045675, A045677, A045678, A128014.

%K nonn

%O 0,5

%A _David W. Wilson_