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I am interested in knowing the "theory" about alternating sequences, (those that have terms where -1 is raised to a power).I need to know things like, if your treatment is algebraic or combinatorial (hey, I can not use anything that has to do with series or analysis).

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I don't see a real question here. – Robin Chapman Sep 29 2010 at 14:36
You can find a treatment which is both algebraic and combinatorial in Solomon W. Golomb's book "Shift Register Sequences". – Moshe Schwartz Sep 29 2010 at 14:55

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