i believe the sequence is actually ...
[1-3 + 2-4 + 3-5 + 4-6 + ... + 885-887 + 886-888]
x A^2

pairing every 2 terms ...
there are 886 pairs
total
= [ 886 x (-2) ] x A^2
= -1772 A^2

alternatively, all the terms cancel out except for the 1st, 3rd, 3rd last, and last terms
total
= [1 + 2 - 887 - 888] x A^2
= -1772 A^2