Suppose for each \( n \in \mathbf{N} \).
\[
\left(1^{2}-a_{1}\right...
Suppose for each \( n \in \mathbf{N} \).
\[
\left(1^{2}-a_{1}\right)+\left(2^{2}-a_{2}\right)+\ldots+\left(n^{2}-a_{n}\right)=\frac{1}{3} n\left(n^{2}-1\right)
\]
then \( a_{n} \) equals
(a) \( n \)
(b) \( n-1 \)
(c) \( n+1 \)
(d) \( 2 n \)
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