If : $\displaystyle \begin{cases} a(4)=2 \\ a(8)=50 \\ a(12)=102 \\a(20)=1104 \end{cases}$ what is $\displaystyle a(n)$ ?
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You haven't defined a sequence. You've only given a few terms. You could use Lagrange interpolation to get a polynomial: $\displaystyle a_n=2\frac{(n-8)(n-12)(n-20)}{(4-8)(4-12)(4-20)}+....$
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