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A045674
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Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, complement and reversed complement.
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12
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1, 1, 2, 2, 4, 4, 6, 8, 12, 16, 20, 32, 38, 64, 72, 128, 140, 256, 272, 512, 532, 1024, 1056, 2048, 2086, 4096, 4160, 8192, 8264, 16384, 16512, 32768, 32908, 65536, 65792, 131072, 131344, 262144, 262656, 524288, 524820, 1048576, 1049600
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OFFSET
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0,3
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LINKS
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FORMULA
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a(2n) = a(n) + 2^(n-1), a(2n+1) = 2^n. - Ralf Stephan, Nov 01 2003
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = If[EvenQ[n], 2^(n/2-1) + a[n/2], 2^((n-1)/2)]; Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Sep 30 2017 *)
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PROG
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(PARI) a(n) = if(n<1, n==0, my(t=0, r=n); while(r%2==0, r=r/2; t+=2^(r-1)); t + 2^(r\2)); \\ Andrew Howroyd, Sep 29 2017
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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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