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My bad. My thoughts were muddled; you're right about the unnecessary index shift. I will delete my comments so as to prevent unnecessary confusions it may serve to procreate to other readers. I had a doubt originally, as to why Pakk mentioned i=1, but never mentioned a term 'i' in argument of the summation, and instead stated $L_{2n}$. Shouldn't it be $L_{2i}$ ?
