3
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I have tried a few basic technique. But it seems still can't come up with a closed form for this sequence ${1, 2, 1, 4, 1, 8, ...}$. See if anyone can give me a hint?

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0
9
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Hint:

  • Find the generating function for 1,1,1,1, ...
  • Deduce the generating function for 1,0,1,0,1,0,1, ...
  • Find the generating function for 2,4,8,16, ...
  • Deduce the generating function for 2,0,4,0,8,0,16, ...
  • Deduce the generating function for 0,2,0,4,0,8,0,16, ...
  • Deduce the generating function you are interested in.
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  • $\begingroup$ I have difficulty from step 3 to step 4 : ( $\endgroup$ Sep 25 '13 at 22:28
  • 1
    $\begingroup$ ohh! $a(x^2)$ ? and then right shift by 1 $\endgroup$ Sep 25 '13 at 22:32
  • $\begingroup$ Indeed. $ $ $ $ $\endgroup$
    – Did
    Sep 25 '13 at 22:36

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