Summation Thug Life!

Algebra Level 3

\[ \large 1^2 - 2^2 + 3^2 - 4^2 + 5^2 - \cdots + (4n-1)^2 - (4n)^2 \]

If the sum above can be expressed in the form of \(an^2 + bn + c \), where \(a,b\) and \(c\) are integer constants, find \(a+b+c\).

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