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%I #22 Sep 23 2019 14:32:46
%S 1,2,6,8,22,32,72,128,278,512,1056,2048,4168,8192,16512,32768,65814,
%T 131072,262656,524288,1049632,2097152,4196352,8388608,16781384,
%U 33554432,67117056,134217728,268451968,536870912,1073774592,2147483648
%N Number of 2n-bead balanced binary strings, rotationally equivalent to complement.
%H Andrew Howroyd, <a href="/A045654/b045654.txt">Table of n, a(n) for n = 0..1000</a>
%H R. Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H R. Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(0)=1, a(2n) = a(n)+2^(2n), a(2n+1) = 2^(2n+1). - _Ralf Stephan_, Jun 07 2003
%F G.f.: 1/(1-x) + sum(k>=0, t(1+2t-2t^2)/(1-t^2)/(1-2t), t=x^2^k). - _Ralf Stephan_, Aug 30 2003
%F For n >= 1, a(n) = sum(0<=k<=A007814(n), 2^(n/2^k)). - _David W. Wilson_, Jan 01 2012
%F Inverse Moebius transform of A045663. - _Andrew Howroyd_, Sep 15 2019
%o (PARI) a(n)={if(n==0, 1, my(s=0); while(n%2==0, s+=2^n; n/=2); s + 2^n)} \\ _Andrew Howroyd_, Sep 22 2019
%Y Cf. A000984, A045653, A045655, A045656, A045663.
%K nonn
%O 0,2
%A _David W. Wilson_
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