\[f(n+2)+7f(n+1)+10f(n)=0\] \[f(0)=2\] \[f(1)=-13\]

If \[f(100)\] can be expressed as \[a(b-3)^{100}-c(102-d)^{100}\] where \( a> 0, b-3>0 , 102-d>0\) and \(c<101\), then what is the value of \((b+c+d)^{a}\)?

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