cp's OEIS Frontend

A045678 Number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement, but not equivalent to their reverse and complement.

%I A045678 #19 Oct 08 2017 10:40:44
%S A045678 0,0,0,2,4,12,26,56,116,240,492,992,2010,4032,8120,16256,32628,65280,
%T A045678 130800,261632,523756,1047552,2096096,4192256,8386522,16773120,
%U A045678 33550272,67100672,134209464,268419072,536854400,1073709056,2147450740
%N A045678 Number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement, but not equivalent to their reverse and complement.
%C A045678 The number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement is A011782(n) and those which are equivalent to their reverse, complement and reversed complement is A045674(n). - _Andrew Howroyd_, Sep 28 2017
%H A045678 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F A045678 a(2n+1) = A020522(n) = 4^n - 2^n. - _Max Alekseyev_, Jan 13 2006
%F A045678 a(n) = A011782(n) - A045674(n). - _Andrew Howroyd_, Sep 28 2017
%t A045678 (* b = A011782, c = A045674 *)
%t A045678 b[0] = 1; b[n_] := 2^(n - 1);
%t A045678 c[0] = 1; c[n_] := c[n] = If[EvenQ[n], 2^(n/2-1) + c[n/2], 2^((n-1)/2)];
%t A045678 a[n_] := b[n] - c[n];
%t A045678 Table[a[n], {n, 0, 32}] (* _Jean-François Alcover_, Oct 08 2017, after _Andrew Howroyd_ *)
%Y A045678 Cf. A011782, A045674.
%K A045678 nonn
%O A045678 0,4
%A A045678 _David W. Wilson_