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A045654
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Number of 2n-bead balanced binary strings, rotationally equivalent to complement.
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9
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1, 2, 6, 8, 22, 32, 72, 128, 278, 512, 1056, 2048, 4168, 8192, 16512, 32768, 65814, 131072, 262656, 524288, 1049632, 2097152, 4196352, 8388608, 16781384, 33554432, 67117056, 134217728, 268451968, 536870912, 1073774592, 2147483648
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0)=1, a(2n) = a(n)+2^(2n), a(2n+1) = 2^(2n+1). - Ralf Stephan, Jun 07 2003
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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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