Summation Thug Life!

Algebra Level 3

1222+3242+52+(4n1)2(4n)2 \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 an2+bn+can^2 + bn + c , where a,ba,b and cc are integer constants, find a+b+ca+b+c.

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