# Closed form of a sequence

• April 12th 2012, 01:02 AM
princeps
Closed form of a sequence
If :

$\begin{cases} a(4)=2 \\ a(8)=50 \\ a(12)=102 \\a(20)=1104 \end{cases}$

what is $a(n)$ ?
• April 12th 2012, 01:42 AM
a tutor
Re: Closed form of a sequence
You haven't defined a sequence. You've only given a few terms.

You could use Lagrange interpolation to get a polynomial:

$a_n=2\frac{(n-8)(n-12)(n-20)}{(4-8)(4-12)(4-20)}+....$