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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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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I have difficulty from step 3 to step 4 : ( – Timothy Leung Sep 25 '13 at 22:28
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1ohh! $a(x^2)$ ? and then right shift by 1 – Timothy Leung Sep 25 '13 at 22:32
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Indeed. $ $ $ $ – Did Sep 25 '13 at 22:36