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http://www.math.psu.edu/vstein/alg/antheory/preprint/andrews/lew4.pdf [Broken]

In page 7, in (21) I don't understand how does changing from q to -q gives the RHS in (5) in page 2, obviously changing gives the LHS in (5), but I don't see how it gives the RHS in (5).

Any tips?

I tried dissecting to sums that passes through all n which are divisble by 2 and all sums that aren't, and noticing that 6n+1=3(2n)+1 , 6n+4=3(2n+1)+1, 6n+2=3(2n)+2, 6n+5=3(2n+1)+2.

but I didn't get far with it.

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# Transforming a sum to another one.

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